Taking a positive integer and squaring it (multiplying it by itself) equals a perfect square.
Example: 3 x 3 = 9 Thus: 9 is a perfect square.
Taking the square root (principal square root) of that perfect square equals the original positive integer.
Example:
√ 9 = 3 Where: 3 is the original integer.
Note: An integer has no fractional or decimal part, and thus a perfect square (which is also an integer) has no fractional or decimal part.
( Perfect Squares List from 1 to 10,000. )
| Positive Integer | Integer Squared= | Perfect Squares List | Square Root of Perfect Square= | Original Integer |
|---|---|---|---|---|
| 1 | 1 ^2 = | 1 | √ 1 = | 1 |
| 2 | 2 ^2 = | 4 | √ 4 = | 2 |
| 3 | 3 ^2 = | 9 | √ 9 = | 3 |
| 4 | 4 ^2 = | 16 | √ 16 = | 4 |
| 5 | 5 ^2 = | 25 | √ 25 = | 5 |
| 6 | 6 ^2 = | 36 | √ 36 = | 6 |
| 7 | 7 ^2 = | 49 | √ 49 = | 7 |
| 8 | 8 ^2 = | 64 | √ 64 = | 8 |
| 9 | 9 ^2 = | 81 | √ 81 = | 9 |
| 10 | 10 ^2 = | 100 | √ 100 = | 10 |
| 11 | 11 ^2 = | 121 | √ 121 = | 11 |
| 12 | 12 ^2 = | 144 | √ 144 = | 12 |
| 13 | 13 ^2 = | 169 | √ 169 = | 13 |
| 14 | 14 ^2 = | 196 | √ 196 = | 14 |
| 15 | 15 ^2 = | 225 | √ 225 = | 15 |
| 16 | 16 ^2 = | 256 | √ 256 = | 16 |
| 17 | 17 ^2 = | 289 | √ 289 = | 17 |
| 18 | 18 ^2 = | 324 | √ 324 = | 18 |
| 19 | 19 ^2 = | 361 | √ 361 = | 19 |
| 20 | 20 ^2 = | 400 | √ 400 = | 20 |
| 21 | 21 ^2 = | 441 | √ 441 = | 21 |
| 22 | 22 ^2 = | 484 | √ 484 = | 22 |
| 23 | 23 ^2 = | 529 | √ 529 = | 23 |
| 24 | 24 ^2 = | 576 | √ 576 = | 24 |
| 25 | 25 ^2 = | 625 | √ 625 = | 25 |
| 26 | 26 ^2 = | 676 | √ 676 = | 26 |
| 27 | 27 ^2 = | 729 | √ 729 = | 27 |
| 28 | 28 ^2 = | 784 | √ 784 = | 28 |
| 29 | 29 ^2 = | 841 | √ 841 = | 29 |
| 30 | 30 ^2 = | 900 | √ 900 = | 30 |
| 31 | 31 ^2 = | 961 | √ 961 = | 31 |
| 32 | 32 ^2 = | 1024 | √ 1024 = | 32 |
| 33 | 33 ^2 = | 1089 | √ 1089 = | 33 |
| 34 | 34 ^2 = | 1156 | √ 1156 = | 34 |
| 35 | 35 ^2 = | 1225 | √ 1225 = | 35 |
| 36 | 36 ^2 = | 1296 | √ 1296 = | 36 |
| 37 | 37 ^2 = | 1369 | √ 1369 = | 37 |
| 38 | 38 ^2 = | 1444 | √ 1444 = | 38 |
| 39 | 39 ^2 = | 1521 | √ 1521 = | 39 |
| 40 | 40 ^2 = | 1600 | √ 1600 = | 40 |
| 41 | 41 ^2 = | 1681 | √ 1681 = | 41 |
| 42 | 42 ^2 = | 1764 | √ 1764 = | 42 |
| 43 | 43 ^2 = | 1849 | √ 1849 = | 43 |
| 44 | 44 ^2 = | 1936 | √ 1936 = | 44 |
| 45 | 45 ^2 = | 2025 | √ 2025 = | 45 |
| 46 | 46 ^2 = | 2116 | √ 2116 = | 46 |
| 47 | 47 ^2 = | 2209 | √ 2209 = | 47 |
| 48 | 48 ^2 = | 2304 | √ 2304 = | 48 |
| 49 | 49 ^2 = | 2401 | √ 2401 = | 49 |
| 50 | 50 ^2 = | 2500 | √ 2500 = | 50 |
| 51 | 51 ^2 = | 2601 | √ 2601 = | 51 |
| 52 | 52 ^2 = | 2704 | √ 2704 = | 52 |
| 53 | 53 ^2 = | 2809 | √ 2809 = | 53 |
| 54 | 54 ^2 = | 2916 | √ 2916 = | 54 |
| 55 | 55 ^2 = | 3025 | √ 3025 = | 55 |
| 56 | 56 ^2 = | 3136 | √ 3136 = | 56 |
| 57 | 57 ^2 = | 3249 | √ 3249 = | 57 |
| 58 | 58 ^2 = | 3364 | √ 3364 = | 58 |
| 59 | 59 ^2 = | 3481 | √ 3481 = | 59 |
| 60 | 60 ^2 = | 3600 | √ 3600 = | 60 |
| 61 | 61 ^2 = | 3721 | √ 3721 = | 61 |
| 62 | 62 ^2 = | 3844 | √ 3844 = | 62 |
| 63 | 63 ^2 = | 3969 | √ 3969 = | 63 |
| 64 | 64 ^2 = | 4096 | √ 4096 = | 64 |
| 65 | 65 ^2 = | 4225 | √ 4225 = | 65 |
| 66 | 66 ^2 = | 4356 | √ 4356 = | 66 |
| 67 | 67 ^2 = | 4489 | √ 4489 = | 67 |
| 68 | 68 ^2 = | 4624 | √ 4624 = | 68 |
| 69 | 69 ^2 = | 4761 | √ 4761 = | 69 |
| 70 | 70 ^2 = | 4900 | √ 4900 = | 70 |
| 71 | 71 ^2 = | 5041 | √ 5041 = | 71 |
| 72 | 72 ^2 = | 5184 | √ 5184 = | 72 |
| 73 | 73 ^2 = | 5329 | √ 5329 = | 73 |
| 74 | 74 ^2 = | 5476 | √ 5476 = | 74 |
| 75 | 75 ^2 = | 5625 | √ 5625 = | 75 |
| 76 | 76 ^2 = | 5776 | √ 5776 = | 76 |
| 77 | 77 ^2 = | 5929 | √ 5929 = | 77 |
| 78 | 78 ^2 = | 6084 | √ 6084 = | 78 |
| 79 | 79 ^2 = | 6241 | √ 6241 = | 79 |
| 80 | 80 ^2 = | 6400 | √ 6400 = | 80 |
| 81 | 81 ^2 = | 6561 | √ 6561 = | 81 |
| 82 | 82 ^2 = | 6724 | √ 6724 = | 82 |
| 83 | 83 ^2 = | 6889 | √ 6889 = | 83 |
| 84 | 84 ^2 = | 7056 | √ 7056 = | 84 |
| 85 | 85 ^2 = | 7225 | √ 7225 = | 85 |
| 86 | 86 ^2 = | 7396 | √ 7396 = | 86 |
| 87 | 87 ^2 = | 7569 | √ 7569 = | 87 |
| 88 | 88 ^2 = | 7744 | √ 7744 = | 88 |
| 89 | 89 ^2 = | 7921 | √ 7921 = | 89 |
| 90 | 90 ^2 = | 8100 | √ 8100 = | 90 |
| 91 | 91 ^2 = | 8281 | √ 8281 = | 91 |
| 92 | 92 ^2 = | 8464 | √ 8464 = | 92 |
| 93 | 93 ^2 = | 8649 | √ 8649 = | 93 |
| 94 | 94 ^2 = | 8836 | √ 8836 = | 94 |
| 95 | 95 ^2 = | 9025 | √ 9025 = | 95 |
| 96 | 96 ^2 = | 9216 | √ 9216 = | 96 |
| 97 | 97 ^2 = | 9409 | √ 9409 = | 97 |
| 98 | 98 ^2 = | 9604 | √ 9604 = | 98 |
| 99 | 99 ^2 = | 9801 | √ 9801 = | 99 |
| 100 | 100 ^2 = | 10000 | √ 10000 = | 100 |