# ROOT

, in Arithmetic and Algebra, denotes a quantity which being multiplied by itself produces some higher power; or a quantity considered as the basis or foundation of a higher power, out of which this arises and grows, like as a plant from its Root.

In the involution of powers, from a given Root, the Root is also called the first power; when this is once multiplied by itself, it produces the square or second power; this multiplied by the Root again, makes the cube or 3d power; and so on. And hence the Roots also come to be denominated the square-Root, or cube-Root, or 2d Root, or 3d Root, &c, according as the given power or quantity is considered as the square, or cube, or 2d power, or 3d power, &c. Thus, 2 is the square-Root or 2d Root of 4, and the cube-Root or 3d Root of 8, and the 4th Root of 16, &c.

Hence, the square-Root is the mean proportional between 1 and the square or given power; and the cube-Root is the first of two mean proportionals between 1 and the given cube; and so on.

To Extract the Root of a given number or power. This is the same thing as to find a number or quantity, which being multiplied the proper number of times, will produce the given number or power. So, to find the cube Root of 8, is finding the number 2, which multiplied twice by itself produces the given number 8.

For the usual methods of extracting the Roots of Numbers, see the common treatises on Arithmetic.

A Root, of any power, that consists of two parts, is called a binomial Root; as 12 or 10 + 2. If it consist of three parts, it is a trinomial Root; as 126 or 100 + 20 + 6. And so on.

The extraction of the Roots of algebraic quantities, is also performed after the same manner as that of numbers; as may be seen in any treatise on algebra. See also the article Extraction of Roots.

A general method for all Roots, is also by Newton's binomial theorem. See Binomial Theorem.

Finite approximating rules for the extraction of Roots have also been given by several authors, as Raphson, De Lagney, Halley, &c. See the articles APPROXIMATION and Extraction. See also Newton's Universal Arith. the Appendix; Philos. Trans. numb. 210, or Abridg. vol. 1, pa. 81; Maclaurin's Alg. pa. 242; Simpson's Alg. pa. 155; or his Essays, pa. 82, or his Dissertations, pa. 102, or his Select Exerc. pa. 215: where various general theorems for approximating to the Roots of pure powers are given. See also Equation and Reduction of Equations, APPROXIMATION, and Converging.

But the most commodious and general rule of any, for such approximations, I believe, is that which has been invented by myself, and explained in my Tracts, vol. 1, pa. 49: which theorem is this; . That is, having to extract the nth Root of the given number N; take an the nearest rational power to that given quantity N, whether greater or less, its Root of the same kind being a; then the required Root, or √nN, will be as is expressed in this formula above; or the same expressed in a proportion will be thus: the Root sought very nearly. Which rule includes all the particular rational formulas of De Lagney, and Halley, which were separately investigated by them; and yet this general formula is perfectly simple and easy to apply, and more easily kept in mind than any one of the said particular formulas.

Ex. Suppose it be required to double the cube, or to extract the cube Root of the number 2.

Here N = 2, n = 3, the nearest Root a = 1, also a3 = 1; hence, for the cube Root the formula becomes .

But ; therefore as 4 : 5 :: 1 : 5/4 = 1.25 = the Root nearly by a first approximation.

Again, for a second approximation, take a = 5/4, and consequently ; therefore as 378 : 381, or as 126 : 127 :: 5/4 : 635/504 = 1.259921 &c, for the required cube Root of 2, which is true even in the last place of decimals.

Root of an Equation, denotes the value of the unknown quantity in an equation; which is such a | quantity, as being substituted instead of that unknown letter, into the equation, shall make all the terms to vanish, or both sides equal to each other. Thus, of the equation , the Root or value of x is 3, because substituting 3 for x, makes it become 9 + 5 = 14. And the Root of the equation is 4, because 2 X 42 = 32. Also the Root of the equation .

For the Nature of Roots, and for extracting the several Roots of equations, see Equation.

Every equation has as many Roots, or values of the unknown quantity, as are the dimensions or highest power in it. As a simple equation one Root, a quadratic two, a cubic three, and so on.

Roots are positive or negative, real or imaginary, rational or radical, &c. See Equation.

Cubic Root. This is threefold, even for a simple cubic. So the cube Root of a3, is either . And even the cube Root of 1 itself is either .

Real and Imaginary Roots. The odd Roots, as the 3d, 5th, 7th, &c Roots, of all real quantities, whether positive or negative, are real, and are respectively positive or negative. So the cube Root of a3 is a, and of - a3 is - a.

But the even Roots, as the 2d, 4th, 6th, &c, are only real when the quantity is positive; being imaginary or impossible when the quantity is negative. So the square Root of a2 is a, which is real; but the square Root of - a2, that is, √(- a2), is imaginary or impossible; because there is no quantity, neither + a nor - a, which by squaring will make the given negative square - a2.

Table of Roots, &c.

THE following Table of Roots, Squares, and Cubes, is very useful in many calculations, and will serve to find square-Roots and cube Roots, as well as square and cubic powers. The Table consists of three columns: in the first column are the series of common numbers, or Roots, 1, 2, 3, 4, 5, 6, &c; in the second column are the squares, and in the third column the cubes of the same. For example, to find the square or the cube of the number or Root 49. Finding this number 49 in the first column; upon the same line with it, stands its square 2401 in the second column, and its cube 117649 in the third column.

Again, to find the square Root of the number 700. Near the beginning of the Table, it appears that the next less and greater tabular squares are 676 and 729, whose Roots are 26 and 27, and therefore the square Root of 700 is between 26 and 27. But a little further on, viz, among the hundreds, it appears that the required Root lies between 26.4 and 26.5, the tabular squares of these being 696.96 and 702.25, cutting off the proper part of the figures for decimals. Take the difference between the less square 696.96 and the given number 700, which gives 3.04, and divide the half of it, viz 1.52, by the less given tabular Root, viz 26.4, and the quotient 575 gives as many more figures of the Root, to be joined to the first three, and thus making the Root equal to 26.4575, which is true in all its places.

Also to find the cube Root of the number 7000; near the beginning of the Table, among the tens, it appears that the cube Root of this number is between 19 and 20; but farther on, among the hundreds, it appears that it lies between 19.1 and 19.2, allowing for the proper number of integers. But if more figures are required; from the given number 7000 take the next less tabular one, or the cube of 19.1, viz 6967871, and there remains 32.129, the 3d part of which, or 10.730, divide by the square of 19.1, viz 364.81, found on the same line, and the quotient 293 is the next three figures of the Root, and therefore the whole cubic Root is 19.1293, which is true in all its figures.—The Table follows. |

 Table of Square and Cubic Roots. Root. Square. Cube. Root. Square. Cube. Root. Square. Cube. Root. Square. Cube. 1 1 1 64 4096 262144 127 16129 2048383 190 36100 6859000 2 4 8 65 4225 274625 128 16384 2097152 191 36481 6967871 3 9 27 66 4356 287496 129 16641 2146689 192 36864 7077888 4 16 64 67 4489 300763 130 16900 2197000 193 37429 7189057 5 25 125 68 4624 314432 131 17161 2248091 194 37636 7301384 6 36 216 69 4761 328509 132 17424 2299968 195 38025 7414875 7 49 343 70 4900 343000 133 17689 2352637 196 38416 7529536 8 64 512 71 5041 357911 134 17956 2406104 197 38809 7645373 9 81 729 72 5184 373248 135 18225 2460375 198 39204 7762392 10 100 1000 73 5329 389017 136 18496 2515456 199 39601 7880599 11 121 1331 74 5476 405224 137 18769 2571353 200 40000 8000000 12 144 1728 75 5625 421875 138 19044 2628072 201 40401 8120601 13 169 2197 76 5776 438976 139 19321 2685619 202 40804 8242408 14 196 2744 77 5929 456533 140 19600 2744000 203 41209 8365427 15 225 3375 78 6084 474552 141 19881 2803221 204 41616 8489664 16 256 4096 79 6241 493039 142 20164 2803288 205 42025 8615125 17 289 4913 80 6400 512000 143 20449 2924207 206 42436 8741816 18 324 5832 81 6561 531441 144 20736 2985984 207 42849 8869743 19 361 6859 82 6724 551368 145 21025 3048625 208 43264 8998912 20 400 8000 83 6889 571787 146 21316 3112136 209 43681 9123329 21 441 9261 84 7056 592704 147 21609 3176523 210 44100 9261000 22 484 10648 85 7225 614125 148 21904 3241792 211 44521 9393931 23 529 12167 86 7396 636056 149 22201 3307949 212 44944 9528128 24 576 13824 87 7569 658503 150 22500 3375000 213 45369 9663597 25 625 15625 88 7744 681472 151 22801 3442951 214 45796 9800344 26 676 17576 89 7921 704969 152 23104 3511808 215 46225 9938375 27 729 19683 90 8100 729000 153 23409 3581577 216 46656 10077696 28 784 21952 91 8281 753571 154 23716 3652264 217 47089 10218313 29 841 24389 92 8464 778688 155 24025 3723875 218 47524 10360282 30 900 27000 93 8649 804357 156 24336 3796416 219 47961 10503459 31 961 29791 94 8836 830584 157 24649 3869893 220 48400 10648000 32 1024 32768 95 9025 857375 158 24964 3944312 221 48841 10793861 33 1089 35937 96 9216 884736 159 25281 4019679 222 49284 10941048 34 1156 39304 97 9409 912673 160 25600 4096000 223 49729 11089567 35 1225 42875 98 9604 941192 161 25921 4173281 224 50176 11239424 36 1296 46656 99 9801 970299 162 26244 4251528 225 50625 11390625 37 1369 50653 100 10000 1000000 163 26569 4330747 226 51076 11543176 38 1444 54872 101 10201 1030301 164 26896 4410944 227 51529 11697083 39 1521 59319 102 10404 1061208 165 27225 4492125 228 51984 11852352 40 1600 64000 103 10609 1092727 166 27556 4574296 229 52441 12008989 41 1681 68921 104 10816 1124864 167 27889 4657463 230 52900 12167000 42 1764 74088 105 11025 1157625 168 28224 4741632 231 53361 12326391 43 1849 79507 106 11236 1191016 169 28561 4826809 232 53824 12487168 44 1936 85184 107 11449 1225043 170 28900 4913000 233 54289 12649337 45 2025 91125 108 11664 1259712 171 29241 5000211 234 54756 12812904 46 2116 97336 109 11881 1295029 172 29584 5088448 235 55225 12977875 47 2209 103823 110 12100 1331000 173 29929 5177717 236 55696 13144256 48 2304 110592 111 12321 1367631 174 30276 5268024 237 56169 13312053 49 2401 117649 112 12544 1404928 175 30625 5359375 238 56644 13481272 50 2500 125000 113 12769 1442897 176 30976 5451776 239 57121 13651919 51 2601 132651 114 12996 1481544 177 31329 5545233 240 57600 13824000 52 2704 140608 115 13225 1520875 178 31684 5639752 241 58081 13997521 53 2809 148877 116 13456 1560896 179 32041 5735339 242 58564 14172488 54 2916 157464 117 13689 1601613 180 32400 5832000 243 59049 14348907 55 3025 166375 118 13924 1643032 181 32761 5929741 244 59536 14526784 56 3136 175616 119 14161 1685159 182 33124 6028568 245 60025 14706125 57 3249 185193 120 14400 1728000 183 33489 6128487 246 60516 14886936 58 3364 195112 121 14641 1771561 184 33856 6229504 247 61009 15069223 59 3481 205379 122 14884 1815848 185 34225 6331625 248 61504 15252992 60 3600 216000 123 15129 1860867 186 34596 6434856 249 62001 15438249 61 3721 226981 124 15376 1906624 187 34969 6539203 250 62500 15625000 62 3844 238328 125 15625 1953125 188 35344 6644672 251 63001 15813251 63 3969 250047 126 15876 2000376 189 35721 6751269 252 63504 16003008
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 Table of Square and Cubic Roots. Root. Square. Cube. Root. Square. Cube. Root. Square. Cube. Root. Square. Cube. 253 64009 16194277 316 99856 31554496 379 143641 54439939 442 195364 86350888 254 64516 16387064 317 100489 31855013 380 144400 54872000 443 196249 86938307 255 65025 16581375 318 101124 32157432 381 145161 55306341 444 197136 87528384 256 65536 16777216 319 101761 32461759 382 145924 55742968 445 198025 88121125 257 66049 16974593 320 102400 327680<*>0 383 146689 5618<*>887 446 198916 88716536 258 66564 17173512 321 103041 33076161 384 147456 56623104 447 199809 89314623 259 67081 17373979 322 103684 33386248 385 148225 57066625 448 200704 89915392 260 67600 17576000 323 104329 33698267 386 148996 57512456 449 201601 90518849 261 68121 17779581 324 104976 34012224 387 149769 57960603 450 202500 91125000 262 68644 17984728 325 105625 34328125 388 150544 58411072 451 203401 91733851 263 69169 18191447 326 106276 34645976 389 151321 58863869 452 204304 92345408 264 69696 18399744 327 106929 34965783 390 152100 59319000 453 205209 92959677 265 70225 18609625 328 107584 35287552 391 152881 59776471 454 206116 93576664 266 70756 18821096 329 108241 35611289 392 153664 60236288 455 207025 94196375 267 71289 19034163 330 108900 35937000 393 154449 60698457 456 207936 94818816 268 71824 19248832 331 109561 36264691 394 155236 61162984 457 208849 95443993 269 72361 19465109 332 110224 36594368 395 156025 61629875 458 209764 96071912 270 72900 19683000 333 110889 36926037 396 156816 62099136 459 210681 96702579 271 73441 19902511 334 111556 37259704 397 157609 62570773 460 211600 97336000 272 73984 20123648 335 112225 37595375 398 158404 63044792 461 212521 97972181 273 74529 20346417 336 112896 37933056 399 159201 63521199 462 213444 98611128 274 75076 20570824 337 113569 38272753 400 160000 64000000 463 214369 99252847 275 75625 20796875 338 114244 386144<*>2 401 160801 64481201 464 215296 99897344 276 76176 21024576 339 114921 38958219 402 161604 64964808 465 216225 100544625 277 76729 21253933 340 115600 39304000 403 162409 65450827 466 217156 101194696 278 77284 21484952 341 116281 39651821 404 163216 65939264 467 218089 101847563 279 77841 21717639 342 116964 40001688 405 164025 66430125 468 219024 102503232 280 78400 21952000 343 117649 40353607 406 164836 66923416 469 219961 103161709 281 78961 22188041 344 118336 40707584 407 165649 67419143 470 220900 103823000 282 79524 22425768 345 119025 41063625 408 166464 67911312 471 221841 104487111 283 80089 22665187 346 119716 41421736 409 167281 68417929 472 222784 105154048 284 80656 22906304 347 120409 41781923 410 168100 68921000 473 223729 105823817 285 81225 23149125 348 121104 42144192 411 168921 69426531 474 224676 106496424 286 81796 23393656 349 121801 42508549 412 169744 69934528 475 225625 107171875 287 82369 23639903 350 122500 42875000 413 170569 70444997 476 226576 107850176 288 82944 23887872 351 123201 43243551 414 171396 70957944 477 227529 108531333 289 83521 24137569 352 123904 43614208 415 172225 71473375 478 228484 109215352 290 84100 24389000 353 124609 43986977 416 173056 71991290 479 229441 109902239 291 84681 24642171 354 125316 44361864 417 173889 72511713 480 230400 110592000 292 85264 24897088 355 126025 44738875 418 174724 73034632 481 231361 111284641 293 85849 25153757 356 126736 45118016 419 175561 73560059 482 232324 111980168 294 86436 25412184 357 127449 45499293 420 176400 74088000 483 233289 112678587 295 87025 25672375 358 128164 45882712 421 177241 74618461 484 234256 113379904 296 87616 25934336 359 128881 46263279 422 178084 75151448 485 235225 114084125 297 88209 26198073 360 129600 46656000 423 178929 75686967 486 236196 114791256 298 88804 26463592 361 130321 47045881 424 179776 76225024 487 237169 115501303 299 89401 26730899 362 131044 47437928 425 180625 76765625 488 238144 116214272 300 90000 27000000 363 131769 47832147 426 181476 77308776 489 239121 116930169 301 90601 27270901 364 132496 48228544 427 182329 77854483 490 240100 117649000 302 91204 27543608 365 133225 48627125 428 183184 78402752 491 241081 118370771 303 91809 27818127 366 133956 49027896 429 184041 78953589 492 242064 119095488 304 92416 28094464 367 134689 49430863 430 184900 79507000 493 243049 119823157 305 93025 28372625 368 135424 49836032 431 185761 80062991 494 244036 120553784 306 93636 28652616 369 136161 50243409 432 186624 80621568 495 245025 121287375 307 94249 28934443 370 136900 50653000 433 187489 81182737 496 246016 122023936 308 94864 29218112 371 137641 51064811 434 188356 81746504 497 247009 122763473 309 95481 29503629 372 138384 51478848 435 189225 82312875 498 248004 123505992 310 96100 29791000 373 139129 51895117 436 190096 82881856 499 249001 124251499 311 96721 30080231 374 139876 52313624 437 190969 83453453 500 250000 125000000 312 97344 30371328 375 140625 52734375 438 191844 84027672 501 251001 125751501 313 97969 30664297 376 141376 53157376 439 192721 84604519 502 252004 126506008 314 98596 30959144 377 142129 53582633 440 193600 85184000 503 253009 127263527 315 99225 31255875 378 142884 54010152 441 194481 85766121 504 254016 128024064
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 Table of Square and Cube Roots. Root. Square. Cube. Root. Square. Cube. Root. Square. Cube. Root. Square. Cube. 505 255025 128787625 568 322624 183250432 631 398161 251239591 694 481636 334255384 506 256036 129554216 569 323761 184220009 632 399424 252435968 695 483025 335702375 507 257049 130323843 570 324900 185193000 633 400689 253636137 696 484416 337153536 508 258064 131096512 571 326041 186169411 634 401956 254840104 697 485809 338608873 509 259081 131872229 572 327184 187149248 635 403225 256047875 698 487204 340068392 510 260100 132651000 573 328329 188132517 636 404496 257259456 699 488601 341532099 511 261121 133432831 574 329476 189119224 637 405769 258474853 700 490000 343000000 512 262144 134217728 575 330625 190109375 638 407044 259694072 701 491401 344472101 513 263169 135005697 576 331776 191102976 639 408321 260917119 702 492804 345948008 514 264196 135796744 577 332929 192100033 640 409600 262144000 703 494209 347428927 515 265225 136590875 578 334084 193100552 641 410881 263374721 704 495616 348913664 516 266256 137388096 579 335241 194104539 642 412164 264609288 705 497025 350402625 517 267289 138188413 580 336400 195112000 643 413449 265847707 706 498436 351895816 518 268324 138991832 581 337561 196122941 644 414736 26<*>089984 707 499849 353393243 519 269361 139798359 582 338724 197137368 645 416025 268336125 708 501264 354894912 520 270400 140608000 583 339889 198155287 646 417316 269586136 709 502681 356400829 521 271441 141420761 584 341056 199176704 647 418609 270840023 710 504100 357911000 522 272484 142236648 585 342225 200201625 648 419904 272097792 711 505521 359425431 523 273529 143055667 586 343396 201230056 649 421201 273359449 712 506944 360944128 524 274576 143877824 587 344569 202262003 650 422500 274625000 713 508369 362467097 525 275625 144703125 588 345744 203297472 651 423801 275894451 714 509796 363994344 526 276676 145531576 589 346921 204336469 652 425104 277167808 715 511225 365525875 527 277729 146363183 590 348100 205379000 653 426409 278445077 716 512656 367061696 528 278784 147197952 591 349281 206425071 654 427716 279726264 717 514089 368601813 529 279841 148035889 592 350464 207474688 655 429025 281011375 718 515524 370146232 530 280900 148877000 593 351649 208527857 656 430336 282300416 719 516961 371694959 531 281961 149721291 594 352836 209584584 657 431649 283593393 720 518400 373248000 532 283024 150568768 595 354025 210644875 658 432964 284890312 721 519841 374805361 533 284089 151419437 596 355216 211708736 659 434281 286191179 722 521284 376367048 534 285156 152273304 597 356409 212776173 660 435600 287496000 723 522729 377933067 535 286225 153130375 598 357604 213847192 661 436921 288804781 724 524176 379503424 536 287296 153990656 599 358801 214921799 662 438244 290117528 725 525625 381078125 537 288369 154854153 600 360000 216000000 663 439569 291434247 726 527076 382657176 538 289444 155720872 601 361201 217081801 664 440896 292754944 727 528529 384240583 539 290521 156590819 602 362404 218167208 665 442225 294079625 728 529984 385828352 540 291600 157464000 603 363609 219256227 666 443556 295408296 729 531441 387420489 541 292681 158340421 604 364816 220348864 667 444889 296740963 730 532900 389017000 542 293764 159220088 605 366025 221445125 668 446224 298077632 731 534361 390617891 543 294849 160103007 606 367236 222545016 669 447561 299418309 732 535824 392223168 544 295936 160989184 607 368449 223648543 670 448900 300763000 733 537289 393832837 545 297025 161878625 608 369664 224755712 671 450241 302111711 734 538756 395446904 546 298116 162771336 609 370881 225866529 672 451584 303464448 735 540225 397065375 547 299209 163667323 610 372100 226981000 673 452929 304821217 736 541696 398688256 548 300304 164566592 611 373321 228099131 674 454276 306182024 737 543169 400315553 549 301401 165469149 612 374544 229220928 675 455625 307546875 738 544644 401947272 550 302500 166375000 613 375769 230346397 676 456976 308915776 739 546121 403583419 551 303601 167284151 614 376996 231475544 677 458329 310288733 740 547600 405224000 552 304704 168196608 615 378225 232608375 678 459684 311665752 741 549081 406869021 553 305809 169112377 616 379456 233744896 679 461041 313046839 742 550564 408518488 554 306916 170031464 617 380689 234885113 680 462400 314432000 743 552049 410172407 555 308025 170953875 618 381924 236029032 681 463761 315821241 744 553536 411830784 556 309136 171879616 619 383161 237176659 682 465124 317214568 745 555025 413493625 557 310249 172808693 620 384400 238328000 683 466489 318611987 746 556516 415160936 558 311364 173741112 621 385641 239483061 684 467856 320013504 747 558009 416832723 559 312481 174676879 622 386884 240641848 685 469225 321419125 748 559504 418508992 560 313600 175616000 623 388129 241804367 686 470596 322828856 749 561001 420189749 561 314721 176558481 624 389376 242970624 687 471969 324242703 750 562500 421875000 562 315844 177504328 625 390625 244140625 688 473344 325660672 751 564001 423564751 563 316969 178453547 626 391876 245314376 689 474721 327082769 752 565504 425259008 564 318096 179406144 627 393129 246491883 690 476100 328509000 753 567009 426957777 565 319225 180362125 628 394384 247673152 691 477481 329939371 754 568516 428661064 566 320356 181321496 629 395641 248858189 692 478864 331373888 755 570025 430368875 567 321489 182284263 630 396900 250047000 693 480249 332812557 756 571536 432081216
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 Table of Square and Cubic Roots. Root Square Cube Root Square Cube Root Square Cube Root Square Cube 757 573049 433798093 820 672400 551368000 883 779689 688465387 946 894916 846590536 758 574564 435519512 821 674041 553387661 884 781456 690807104 947 896809 849378123 759 576081 437245479 822 675684 555412248 885 783225 693154125 948 898704 851971392 760 577600 438976000 823 677329 557441767 886 784996 695506456 949 900601 854670349 761 579121 440711081 824 678976 559476224 887 786769 697864103 950 902500 857375000 762 580644 442450728 825 680625 561515625 888 788544 700227072 951 904401 860085351 763 582169 444194947 826 682276 563559976 889 790321 702595369 952 906304 862801408 764 583696 445943744 827 683920 565609283 890 792100 704969000 953 908209 865523177 765 585225 447697125 828 685584 567663552 891 793881 707347971 954 910116 868250664 766 586756 449455096 829 687241 569722789 892 795664 709732288 955 912025 870983875 767 588289 451217663 830 688900 571787000 893 797449 712121957 956 913936 873722816 768 589824 452984832 831 690561 573856191 894 799236 714516984 957 915849 876467493 769 591361 454756609 832 692224 575930368 895 801025 716917375 958 917764 879217912 770 592900 456533000 833 693889 578009537 896 802816 719323136 959 919681 881974079 771 594441 458314011 834 695556 580093704 897 804609 721734273 960 921600 884736000 772 595984 460099648 835 697225 582182875 898 806404 724150792 961 923521 887503681 773 597529 461889917 836 698896 584277056 899 808201 726572699 962 925444 890277128 774 599076 463684824 837 700569 586376253 900 810000 729000000 963 927369 893056347 775 600625 465484375 838 702244 588480472 901 811801 731432701 964 929296 895841344 776 602176 467288576 839 703921 590589719 902 813604 733870808 965 931225 898632125 777 603729 469097433 840 705600 592704000 903 815409 736314327 966 933156 901428696 778 605284 470910952 841 707281 594823321 904 817216 738763264 967 935089 904231063 779 606841 472729139 842 708964 596947688 905 819025 741217625 968 937024 907039232 780 608400 474552000 843 710649 599077107 906 820836 743677416 969 938961 909853209 781 609961 476379541 844 712336 601211584 907 822649 746142643 970 940900 912673000 782 611524 478211768 845 714025 603351125 908 824464 748613312 971 942841 915498611 783 613089 480048687 846 715716 605495736 909 826281 751089429 972 944784 9183300<*>8 784 614656 481890304 847 717409 607645423 910 828100 753571000 973 946729 921167317 785 616225 483736625 848 719104 609800192 911 829921 756058031 974 948676 924010424 786 617796 485587656 849 720801 611960049 912 831744 758550528 975 950625 926859375 787 619369 487443403 850 722500 614125000 913 833569 761048497 976 952576 929714176 788 620944 489303872 851 724201 616295051 914 835396 763551944 977 954529 932574833 789 622521 491169069 852 725904 618470208 915 837225 766060875 978 956484 935441352 790 624100 493039000 853 727609 620650477 916 839056 768575296 979 958441 938313739 791 625681 494913671 854 729316 622835864 917 840889 771095213 980 960400 941192001 792 627264 496793088 855 731025 625026375 918 842724 773620632 981 962361 944076141 793 628849 498677257 856 732736 627222016 919 844561 776151559 982 964324 946966168 794 630436 500566184 857 734449 629422793 920 846400 778688000 983 966289 949862087 795 632025 502459875 858 736164 631628712 921 848241 781229961 984 968256 952763904 796 633616 504358336 859 737881 633839779 922 850084 783777448 985 970225 955671625 797 635209 506261573 860 739600 636056000 923 851929 786330467 986 972196 958585256 798 636804 508169592 861 741321 638277381 924 853776 788889024 987 974169 961504803 799 638401 510082399 862 743044 640503928 925 855625 791453125 988 976144 964430272 800 640000 512000000 863 744769 642735647 926 857476 794022776 989 978121 967<*>61669 801 641601 513922401 864 746496 644972544 927 859329 796597983 990 980100 970299000 802 643204 515849608 865 748225 647214625 928 861184 799178752 991 982081 973242271 803 644809 517781627 866 749956 649461896 929 863041 801765089 992 984064 976191488 804 646416 519718464 867 751689 651714363 930 864900 804357000 993 986049 979146657 805 648025 521660125 868 753424 653972032 931 866761 806954491 994 988036 982107784 806 649636 523606616 869 755161 656234909 932 868624 809557568 995 990025 985074875 807 651249 525557943 870 756900 658503000 933 870489 812166237 996 992016 988047936 808 652864 527514112 871 758641 660776311 934 872356 814780504 997 994009 991026973 809 654481 529475129 872 760384 663054848 935 874225 817400375 998 996004 994011992 810 656100 531441000 873 762129 665338617 936 876096 820025856 999 993001 997002999 811 657721 533411731 874 763876 667627624 937 877969 822656953 1000 1000000 1000000000 812 659344 535387328 875 765625 669921875 938 879844 825293672 1001 1002001 1003003001 813 660969 537366797 876 767376 672221376 939 881721 827936019 1002 1004004 1006012008 814 662596 539353144 877 769129 674526133 940 883600 830584000 1003 1006009 1009027027 815 664225 541343375 878 770884 676836152 941 885481 833237621 1004 1008016 1012048064 816 665856 543338496 879 772641 679151439 942 887364 835896888 1005 1010025 1015075125 817 667489 545338513 880 774400 681472000 943 889249 838561807 1006 1012036 1018108216 818 669124 547343432 881 776161 683797841 944 891136 841232384 1007 1014049 1021147343 819 670761 549353259 882 777924 686128968 945 893025 843908625 1008 1016064 1024192512
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The following is another Table of the Square Roots of the first 1000 Numbers to 10 places of decimal figures beside the integers, which needs no farther explanation, as Numbers stand always in the first column, and their Square Roots in the next.

 Table of Square Roots to ten Decimal Places. No. Square Root. No. Square Root. No. Square Root. No. Square Root. 1 1.0000000000 64 8.0000000000 127 11.2694276696 190 13.7840487521 2 1.4142135624 65 8.0622577483 128 11.3137084990 191 13.8202749611 3 1.7320508076 66 8.1240384046 129 11.3578166916 192 13.8564064606 4 2.0000000000 67 8.1853527719 130 11.4017542510 193 13.8924439894 5 2.2360679775 68 8.2462112512 131 11.4455231423 194 13.9283882772 6 2.4494897428 69 8.3066238629 132 11.4891252931 195 13.9642400438 7 2.6457513111 70 8.3666002653 133 11.5325625947 196 14.0000000000 8 2.8284271247 71 8.4261497732 134 11.5758369028 197 14.0356688441 9 3.0000000000 72 8.4852813742 135 11.6189500386 198 14.0712472795 10 3.1622776602 73 8.5440037453 136 11.6619037897 199 14.1067359797 11 3.3166247904 74 8.6023252670 137 11.7046999111 200 14.1421356237 12 3.4641016151 75 8.6602540378 138 11.7473443808 201 14.1774468788 13 3.6055512755 76 8.7177978871 139 11.7898261226 202 14.2126704036 14 3.7416573868 77 8.7749643874 140 11.8321595662 203 14.2478068488 15 3.8729833462 78 8.8317608663 141 11.8743420870 204 14.2828568571 16 4.0000000000 79 8.8881944173 142 11.9163752878 205 14.3178210633 17 4.1231056256 80 8.9442719100 143 11.9582607431 206 14.3527000944 18 4.2426406871 81 9.0000000000 144 12.0000000000 207 14.3874945699 19 4.3588989435 82 9.0553851381 145 12.0415945788 208 14.4222051019 20 4.4721359550 83 9.1104335791 146 12.0830459736 209 14.4568322948 21 4.5825756950 84 9.1651513899 147 12.1243556530 210 14.4913767462 22 4.6904157598 85 9.2195444573 148 12.1655250606 211 14.5258390463 23 4.7958315233 86 9.2736184955 149 12.2065556153 212 14.5602197786 24 4.8989794856 87 9.3273790531 150 12.2474487139 213 14.5945195193 25 5.0000000000 88 9.3808315196 151 12.2882057274 214 14.6287388383 26 5.0990195136 89 9.4339811321 152 12.3288280059 215 14.6628782986 27 5.1961524227 90 9.4868329805 153 12.3693168769 216 14.6969384567 28 5.2915026221 91 9.5393920142 154 12.4096736460 217 14.7309198627 29 5.3851648071 92 9.5916630466 155 12.4498995980 218 14.7648230602 30 5.4772255751 93 9.6436507610 156 12.4899959968 219 14.7986485869 31 5.5677643628 94 9.6953597148 157 12.5299640861 220 14.8323969742 32 5.6568542495 95 9.7467943448 158 12.5698050900 221 14.8660687473 33 5.7445626465 96 9.7979589711 159 12.6095202129 222 14.8996644258 34 5.8309518948 97 9.8488578018 160 12.6491106407 223 14.9331845231 35 5.9160797831 98 9.8994949366 161 12.6885775404 224 14.9666295471 36 6.0000000000 99 9.9498743711 162 12.7279220614 225 15.0000000000 37 6.0827625303 100 10.0000000000 163 12.7671453348 226 15.0332963784 38 6.1644140030 101 10.0498756211 164 12.8062484749 227 15.0665191733 39 6.2449979984 102 10.0995049384 165 12.8452325787 228 15.0996688705 40 6.3245553203 103 10.1488915651 166 12.8840987267 229 15.1327459504 41 6.4031242374 104 10.1980390272 167 12.9228479833 230 15.1657508881 42 6.4807406984 105 10.2469507660 168 12.9614813968 231 15.1986841536 43 6.5574385243 106 10.2956301410 169 13.0000000000 232 15.2315462117 44 6.6332495807 107 10.3440804328 170 13.0384048104 233 15.2643375225 45 6.7082039325 108 10.3923048454 171 13.0766968306 234 15.2970585408 46 6.7823299831 109 10.4403065089 172 13.1148770486 235 15.3297097168 47 6.8556546004 110 10.4880884817 173 13.1529464380 236 15.3622914957 48 6.9282032303 111 10.5356537529 174 13.1909059583 237 15.3948043183 49 7.0000000000 112 10.5830052443 175 13.2287565553 238 15.4272486209 50 7.0710678119 113 10.6301458127 176 13.2664991614 239 15.4596248337 51 7.1414284285 114 10.6770782520 177 13.3041346957 240 15.4919333848 52 7.2111025509 115 10.7238052948 178 13.3416640641 241 15.5241746963 53 7.2801098893 116 10.7703296143 179 13.3790881603 242 15.5563491861 54 7.3484692283 117 10.8166538264 180 13.4164078650 243 15.5884572681 55 7.4161984871 118 10.8627804912 181 13.4586240471 244 15.6204993518 56 7.4833147<*>35 119 10.9087121146 182 13.4907375632 245 15.6524758425 57 7.5498344353 120 10.9544511501 183 13.5277492585 246 15.6843871414 58 7.6157731059 121 11.0000000000 184 13.5646599663 247 15.7162336455 59 7.6811457479 122 11.0453610172 185 13.6014705087 248 15.7480157480 60 7.7459666924 123 11.0905365064 186 13.6381816970 249 15.7797338381 61 7.8102496759 124 11.1355287257 187 13.6747943312 250 15.8113883008 62 7.8740078740 125 11.1803398875 188 13.7113092008 251 15.8429795178 63 7.9372539332 126 11.2249721603 189 13.7477270849 252 15.8745078664
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 Table of Square Roots. No. Square Root. No. Square Root. No. Square Root. No. Square Root. 253 15.9059737206 316 17.7763888346 379 19.4679223339 442 21.0237960416 254 15.9373774505 317 17.8044938148 380 19.4935886896 443 21.0475651798 255 15.9687194227 318 17.8325545001 381 19.5192212959 444 21.0713075057 256 16.0000000000 319 17.8605710995 382 19.5448202857 445 21.0950231097 257 16.0312195419 320 17.8885438200 383 19.5703857908 446 21.1187120819 258 16.0623784042 321 17.9164728672 384 19.5959179423 447 21.1423745119 259 16.0934769394 322 17.9443584449 385 19.6214168703 448 21.1660104885 260 16.1245154966 323 17.9722007556 386 19.6468827044 449 21.1896201004 261 16.1554944214 324 18.0000000000 387 19.6723155729 450 21.2132034356 262 16.1864140562 325 18.0277563773 388 19.6977156036 451 21.2367605816 263 16.2172747402 326 18.0554700853 389 19.7230829231 452 21.2602916255 264 16.2480768092 327 18.0831413200 390 19.7484176581 453 21.2837966538 265 16.2788205961 328 18.1107702763 391 19.7737199333 454 21.3072757527 266 16.3095064303 329 18.1383571472 392 19.7989898732 455 21.3307290077 267 16.3401346384 330 18.1659021246 393 19.8242276016 456 21.3541565041 268 16.3707055437 331 18.1934053987 394 19.8494332413 457 21.3775583264 269 16.4012194669 332 18.2208671583 395 19.8746069144 458 21.4009345590 270 16.4316767252 333 18.2482875909 396 19.8997487421 459 21.4242852856 271 16.4620776332 334 18.2756668825 397 19.9248588452 460 21.4476105895 272 16.4924225025 335 18.3030052177 398 19.9499373433 461 21.4709105536 273 16.5227116419 336 18.3303027798 399 19.9749843554 462 21.4941852579 274 16.5529453569 337 18.3575597507 400 20.0000000000 463 21.5174347914 275 16.5831239518 338 18.3847763109 401 20.0249843945 464 21.5406592285 276 16.6132477258 339 18.4119526395 402 20.0499376558 465 21.5638586528 277 16.6433169771 340 18.4390889146 403 20.0748598999 466 21.5870331449 278 16.6733320005 341 18.4661853126 404 20.0997512422 467 21.6101827850 279 16.7032930885 342 18.4932420089 405 20.1246117975 468 21.6333076528 280 16.7332005307 343 18.5202591775 406 20.1494416796 469 21.6564078277 281 16.7630546142 344 18.5472369910 407 20.1742410018 470 21.6794833887 282 16.7928556237 345 18.5741756210 408 20.1990098767 471 21.7025344142 283 16.8226038413 346 18.6010752377 409 20.2237484162 472 21.7255609824 284 16.8522995464 347 18.6279360102 410 20.2484567313 473 21.7485631709 285 16.8819430161 348 18.6547581062 411 20.2731349327 474 21.7715410571 286 16.9115345253 349 18.6815416923 412 20.2977831302 475 21.7944947177 287 16.9410743461 350 18.7082869339 413 20.3224014329 476 21.8174242293 288 16.9705627485 351 18.7349939952 414 20.3469899494 477 21.8403296678 289 17.0000000000 352 18.7616630393 415 20.3715487875 478 21.8632111091 290 17.0293863659 353 18.7882942281 416 20.3960780544 479 21.8860686282 291 17.0587221092 354 18.8148877222 417 20.4205778567 480 21.9089023002 292 17.0880074906 355 18.8414436814 418 20.4450483003 481 21.9317121995 293 17.1172427686 356 18.8679622641 419 20.4694894905 482 21.9544984024 294 17.1464281995 357 18.8944436277 420 20.4939015319 483 21.9772609758 295 17.1755640373 358 18.9208879284 421 20.5182845287 484 22.0000000000 296 17.2046505341 359 18.9472953215 422 20.5426385842 485 22.0227155455 297 17.2336879396 360 18.9736659610 423 20.5669638012 486 22.0454076850 298 17.2626765016 361 19.0000000000 424 20.5912602820 487 22.0680764907 299 17.2916164658 362 19.0262975904 425 20.6155281281 488 22.0907220344 300 17.3205080757 363 19.0525588833 426 20.6397674406 489 22.1133443875 301 17.3493515729 364 19.0787840283 427 20.6639783198 490 22.1359436212 302 17.3781471969 365 19.1049731745 428 20.6881608656 491 22.1585198062 303 17.4068951855 366 19.1311264697 429 20.7123151772 492 22.1810730128 304 17.4355957742 367 19.1572440607 430 20.7364413533 493 22.2036033112 305 17.4642491966 368 19.1833260933 431 20.7605394920 494 22.2261107709 306 17.4928556845 369 19.2093727123 432 20.7846096908 495 22.2485954613 307 17.5214154679 370 19.2353840617 433 20.8086520467 496 22.2710574513 308 17.5499287748 371 19.2613602843 434 20.8326666560 497 22.2934968096 309 17.5783958312 372 19.2873015220 435 20.8566536146 498 22.3159136044 310 17.6068168617 373 19.3132079158 436 20.8806130178 499 22.3383079039 311 17.6351920885 374 19.3390537514 437 20.9045449604 500 22.3606797750 312 17.6635217327 375 19.3649167310 438 20.9284495365 501 22.3830292856 313 17.6918060130 376 19.3907194297 439 20.9523268398 502 22.4053565024 314 17.7200451467 377 19.4164878389 440 20.9761769<*>34 503 22.4276614920 315 17.7482393493 378 19.4422220952 441 21.0000000000 504 22.4499441206
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 Table of Square Roots. No. Square Root. No. Square Root. No. Square Root. No. Square Root. 505 22.4722050542 568 23.8327505756 631 25.1197133742 694 26.3438797446 506 22.4944437584 569 23.8537208838 632 25.1396101800 695 26.3628526529 507 22.5166604984 570 23.8746727726 633 25.1594912508 696 26.3818119165 508 22.5388553392 571 23.8956062907 634 25.1793566201 697 26.4007575649 509 22.5610283454 572 23.9165214862 635 25.1992063367 698 26.4196896272 510 22.5831795813 573 23.9374184072 636 25.2190404258 699 26.4386081328 511 22.6053091109 574 23.9582971014 637 25.2388589282 700 26.4575131106 512 22.6274169980 575 23.9791576166 638 25.2586618806 701 26.4764045897 513 22.6495033058 576 24.0000000000 639 25.2784493195 702 26.4952825990 514 22.6715680975 577 24.0208242989 640 25.2982212813 703 26.5141471671 515 22.6936114358 578 24.0416305603 641 25.3179778023 704 26.5329983228 516 22.7156333832 579 24.0624188310 642 25.3377189186 705 26.5518360947 517 22.7376340018 580 24.0831683962 643 25.3574446662 706 26.4706605112 518 22.7596133535 581 24.1039415864 644 25.3771550809 707 26.5894716006 519 22.7815714998 582 24.1246761636 645 25.3968501984 708 26.6082693913 520 22.8035085020 583 24.1453929353 646 25.4165300543 709 26.6270539114 521 22.8254244210 584 24.1660919472 647 25.4361946840 710 26.6458251889 522 22.8473193176 585 24.1867732449 648 25.4558441227 711 26.6645832519 523 22.8691932521 586 24.2074368736 649 25.4754784057 712 26.6833281283 524 22.8910462845 587 24.2280828792 650 25.4950975680 713 26.7020598456 525 22.9128784748 588 24.2487113060 651 25.5147016443 714 26.7207784318 526 22.9346898824 589 24.2693221990 652 25.5342906696 715 26.7394839142 527 22.9564805665 590 24.2899156030 653 25.5538646784 716 26.7581763205 528 22.9782505862 591 24.3104915623 654 25.5734237051 717 26.7768556780 529 23.0000000000 592 24.3310501212 655 25.5929677841 718 26.7955220139 530 23.0217288664 593 24.3515913238 656 25.6124969497 719 26.8141753556 531 23.0434372436 594 24.3721152139 657 25.6320112360 720 26.8328157300 532 23.0651251893 595 24.3926218353 658 25.6515106768 721 26.8514431642 533 23.0867927612 596 24.4131112315 659 25.6709953060 722 26.8700576851 534 23.1084400166 597 24.4335834457 660 25.6904651573 723 26.8886593195 535 23.1300670124 598 24.4540385213 661 25.7099202644 724 26.9072480941 536 23.1516738056 599 24.4744765010 662 25.7293606605 725 26.9258240357 537 23.1732604525 600 24.4948974278 663 25.7487863792 726 26.9443871706 538 23.1948270095 601 24.5153013443 664 25.7681974535 727 26.9629375254 539 23.2163735325 602 24.5356882928 665 25.7875939165 728 26.9814751265 540 23.2379000772 603 24.5560583156 666 25.8069758011 729 27.0000000000 541 23.2594066992 604 24.5764114549 667 25.8263431403 730 27.0185121722 542 23.2808934536 605 24.5967477525 668 25.8456959666 731 27.0370116692 543 23.3023603955 606 24.6170672502 669 25.8650343128 732 27.0554985169 544 23.3238075794 607 24.6373699895 670 25.8843582111 733 27.0739727414 545 23.3452350599 608 24.6576560119 671 25.9036676940 734 27.0924343683 546 23.3666428911 609 24.6779253585 672 25.9229627936 735 27.1108834235 547 23.3880311271 610 24.6981780705 673 25.9422435421 736 27.1293199325 548 23.4093998214 611 24.7184141886 674 25.9615099715 737 27.1477439210 549 23.4307490277 612 24.7386337537 675 25.9807621135 738 27.1661554144 550 23.4520787991 613 24.7588368063 676 26.0000000000 739 27.1845544381 551 23.4733891886 614 24.7790233867 677 26.0192236625 740 27.2029410175 552 23.4946802489 615 24.7991935353 678 26.0384331326 741 27.2213151776 553 23.5159520326 616 24.8193472920 679 26.0576284416 742 27.2396769438 554 23.5372045919 617 24.8394846967 680 26.0768096208 743 27.2580263409 555 23.5584379788 618 24.8596057893 681 26.0959767014 744 27.2763633940 556 23.5796522451 619 24.8797106092 682 26.1151297144 745 27.2946881279 557 23.6008474424 620 24.8997991960 683 26.1342686907 746 27.3130005675 558 23.6220236220 621 24.9198715888 684 26.1533936612 747 27.3313007374 559 23.6431808351 622 24.9399278267 685 26.1725046566 748 27.3495886624 560 23.6643191324 623 24.9599679487 686 26.1916017074 749 27.3678643668 561 23.6854385647 624 24.9799919936 687 26.2106848442 750 27.3861278753 562 23.7065391823 625 25.0000000000 688 26.2297540972 751 27.4043792121 563 23.7276210354 626 25.0199920064 689 26.2488094968 752 27.4226184016 564 23.7486841741 627 25.0399680511 690 26.2678510731 753 27.4408454680 565 23.7697286480 628 25.0599281723 691 26.2868788562 754 27.4590604355 566 23.7907545067 629 25.0798724080 692 26.3058928759 755 27.4772633281 567 23.8117617996 630 25.0998007960 693 26.3248931622 756 27.4954541697
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 Table of Square Roots. No. Square Root. No. Square Root. No. Square Root. No. Square Root. 757 27.5136329844 818 28.6006992922 879 29.6479324743 940 30.6594194335 758 27.5317997959 819 28.6181760425 880 29.6647939484 941 30.6757233004 759 27.5499546279 820 28.6356421266 881 29.6816441593 942 30.6920185064 760 27.5680975042 821 28.6530975638 882 29.6984848098 943 30.7083050656 761 27.5862284483 822 28.6705423737 883 29.7153159162 944 30.7245829915 762 27.6043474837 823 28.6879765756 884 29.7321374946 945 30.7408522979 763 27.6224546339 824 28.7054001888 885 29.7489495613 946 30.7571129985 764 27.6405499222 825 28.7228132327 886 29.7657521323 947 30.7733651069 765 27.6586333719 826 28.7402157264 887 29.7825452237 948 30.7896086367 766 27.6767050062 827 28.7576076891 888 29.7993288515 949 30.8058436015 767 27.6947648483 828 28.7749891399 889 29.8161030318 950 30.8220700148 768 27.7128129211 829 28.7923600978 890 29.8328677804 951 30.8382878902 769 27.7308492477 830 28.8097205818 891 29.8496231132 952 30.8544972417 770 27.7488738510 831 28.8270706108 892 29.8663690461 953 30.8706980809 771 27.7668867538 832 28.8444102037 893 29.8831055950 954 30.8868904230 772 27.7848879789 833 28.8617393793 894 29.8998327755 955 30.9030742807 773 27.8028775489 834 28.8790581564 895 29.9165506033 956 30.9192496675 774 27.8208554865 835 28.8963665536 896 29.9332590942 957 30.9354165965 775 27.8388218142 836 28.9136645896 897 29.9499582637 958 30.9515750811 776 27.8567765544 837 28.9309522830 898 29.9666481275 959 30.9677251344 777 27.8747197295 838 28.9482296523 899 29.9833287011 960 30.9838667697 778 27.8926513620 839 28.9654967159 900 30.0000000000 961 31.0000000000 779 27.9105714739 840 28.9827534924 901 30.0166620396 962 31.0161248385 780 27.9284800875 841 29.0000000000 902 30.0333148354 963 31.0322412984 781 27.9463772250 842 29.0172362571 903 30.0499584026 964 31.0483493925 782 27.9642629082 843 29.0344622819 904 30.0665927567 965 31.0644491340 783 27.9821371593 844 29.0516780927 905 30.0832179130 966 31.0805405358 784 28.0000000000 845 29.0688837075 906 30.0998338866 967 31.0966236109 785 28.0178514522 846 29.0860791445 907 30.1164406928 968 31.1126983722 786 28.0356915378 847 29.1032644217 908 30.1330383466 969 31.1287648325 787 28.0535202782 848 29.1204395571 909 30.1496268634 970 31.1448230048 788 28.0713376881 849 29.1376045687 910 30.1662062580 971 31.1608729018 789 28.0891438104 850 29.1547594742 911 30.1827765456 972 31.1769145362 790 28.1069386451 851 29.1719042916 912 30.1993377411 973 31.1929479210 791 28.1247222209 852 29.1890390387 913 30.2158898595 974 31.2089730687 792 28.1424945589 853 29.2061637330 914 30.2324329157 975 31.2249899920 793 28.1602556807 854 29.2232783924 915 30.2489669245 976 31.2409987036 794 28.1780056072 855 29.2403830344 916 30.2654919008 977 31.2569992162 795 28.1957443597 856 29.2574776767 917 30.2820078595 978 31.2729915422 796 28.2134719593 857 29.2745623366 918 30.2985148151 979 31.2889756943 797 28.2311884270 858 29.2916370318 919 30.3150127824 980 31.3049516850 798 28.2488937837 859 29.3087017795 920 30.3315017762 981 31.3209195267 799 28.2665880502 860 29.3257565972 921 30.3479818110 982 31.3368792320 800 28.2842712475 861 29.3428015022 922 30.3644529014 983 31.3528308132 801 28.3019433962 862 29.3598365118 923 30.3809150619 984 31.3687742827 802 28.3196045170 863 29.3768616431 924 30.3973683071 985 31.3847096530 803 28.3372546306 864 29.3938769134 925 30.4138126515 986 31.4006369362 804 28.3548937575 865 29.4108823397 926 30.4302481094 987 31.4165561448 805 28.3725219182 866 29.4278779391 927 30.4466746953 988 31.4324672910 806 28.3901391332 867 29.4448637287 928 30.4630924235 989 31.4483703870 807 28.4077454227 868 29.4618397253 929 30.4795013083 990 31.4642654451 808 28.4253408071 869 29.4788059460 930 30.4959013640 991 31.4801524774 809 28.4429253067 870 29.4957624075 931 30.5122926048 992 31.4960314960 810 28.4604989415 871 29.5127091267 932 30.5286750449 993 31.5119025132 811 28.4780617318 872 29.5296461205 933 30.5450486986 994 31.5277655409 812 28.4956136976 873 29.5465734054 934 30.5614135799 995 31.5436205912 813 28.5131548588 874 29.5634909982 935 30.5777697028 996 31.5594676761 814 28.5306852354 875 29.5803989155 936 30.5941170816 997 31.5753068077 815 28.5482048472 876 29.5972971739 937 30.6104557300 998 31.5911379979 816 28.5657137142 877 29.6141857899 938 30.6267856622 999 31.6069612586 817 28.5832118559 878 29.6310647801 939 30.6431068921 1000 31.6227766017
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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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