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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 table 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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