Square Root Conversion Tables

How to convert an integer to its square root using the tables below:

1)  Find a value in the column labeled X.

2)  The square root of that integer is beside X in the middle column labeled √ X.

3)  The third column is X2 and is the result of ( X ) × ( X ).

 X √X X2 X3 1 1 1 1 2 1.4142135 4 8 3 1.7320508 9 27 4 2 16 64 5 2.2360679 25 125 6 2.4494897 36 216 7 2.6457513 49 343 8 2.8284271 64 512 9 3 81 729 10 3.1622776 100 1,000 11 3.3166247 121 1,331 12 3.4641016 144 1,728 13 3.6055512 169 2,197 14 3.7416573 196 2,744 15 3.8729833 225 3,375 16 4 256 4,096 17 4.1231056 289 4,913 18 4.2426406 324 5,832 19 4.3588989 361 6,859 20 4.4721359 400 8,000 21 4.5825756 441 9,261 22 4.6904157 484 10,648 23 4.7958315 529 12,167 24 4.8989794 576 13,824 25 5 625 15,625 26 5.0990195 676 17,576 27 5.1961524 729 19,683 28 5.2915026 784 21,952 29 5.3851648 841 24,389 30 5.4772255 900 27,000 31 5.5677643 961 29,791 32 5.6568542 1,024 32,768 33 5.7445626 1,089 35,937 34 5.8309518 1,156 39,304 35 5.9160797 1,225 42,875 36 6 1,296 46,656 37 6.0827625 1,369 50,653 38 6.164414 1,444 54,872 39 6.2449979 1,521 59,319 40 6.3245553 1,600 64,000 41 6.4031242 1,681 68,921 42 6.4807406 1,764 74,088 43 6.5574385 1,849 79,507 44 6.6332495 1,936 85,184 45 6.7082039 2,025 91,125 46 6.7823299 2,116 97,336 47 6.8556546 2,209 103,823 48 6.9282032 2,304 110,592 49 7 2,401 117,649 50 7.0710678 2,500 125,000
 X √X X2 X3 51 7.1414284 2,601 132,651 52 7.2111025 2,704 140,608 53 7.2801098 2,809 148,877 54 7.3484692 2,916 157,464 55 7.4161984 3,025 166,375 56 7.4833147 3,136 175,616 57 7.5498344 3,249 185,193 58 7.6157731 3,364 195,112 59 7.6811457 3,481 205,379 60 7.7459666 3,600 216,000 61 7.8102496 3,721 226,981 62 7.8740078 3,844 238,328 63 7.9372539 3,969 250,047 64 8 4,096 262,144 65 8.0622577 4,225 274,625 66 8.1240384 4,356 287,496 67 8.1853527 4,489 300,763 68 8.2462112 4,624 314,432 69 8.3066238 4,761 328,509 70 8.3666002 4,900 343,000 71 8.4261497 5,041 357,911 72 8.4852813 5,184 373,248 73 8.5440037 5,329 389,017 74 8.6023252 5,476 405,224 75 8.660254 5,625 421,875 76 8.7177978 5,776 438,976 77 8.7749643 5,929 456,533 78 8.8317608 6,084 474,552 79 8.8881944 6,241 493,039 80 8.9442719 6,400 512,000 81 9 6,561 531,441 82 9.0553851 6,724 551,368 83 9.1104335 6,889 571,787 84 9.1651513 7,056 592,704 85 9.2195444 7,225 614,125 86 9.2736184 7,396 636,056 87 9.327379 7,569 658,503 88 9.3808315 7,744 681,472 89 9.4339811 7,921 704,969 90 9.4868329 8,100 729,000 91 9.539392 8,281 753,571 92 9.591663 8,464 778,688 93 9.6436507 8,649 804,357 94 9.6953597 8,836 830,584 95 9.7467943 9,025 857,375 96 9.7979589 9,216 884,736 97 9.8488578 9,409 912,673 98 9.8994949 9,604 941,192 99 9.9498743 9,801 970,299 100 10 10,000 1,000,000

For any value of X:

1)    X = √ X × √ X

2)    X equals √ X2

3)    X2 = ( X ) × ( X )

4)    X2 = √ X × √ X × √ X × √ X

X equals 56 in the following example:

(The square root of 56 is 7.4833147)

1)    56 = 7.4833147 × 7.4833147

2)    56 = √ 3,136

3)    3,136 = 56 × 56

4)    3,136 = 7.4833147 × 7.4833147 × 7.4833147 × 7.4833147

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