Square Root Calculator
Last updated: July 6, 2022
What is a Square Root?
For example, 16 are square root of 256, because 162 = 256.
Square root of 400 = 20, because 202 = 400.
To calculate the cube root, use the Cube Roots Calculator.
For example, square root of 9 denoted as √9.
Perfect Square Calculator
For example, 1, 4, 9, 25, 100 and 121 are perfect squares while 3, 5, 12, 23 and 53 are not.
25 is a perfect square because 5 * 5 = 52 = 25.
75 is a not perfect square because it cannot be expressed as the product of two same integers.
Simplify Square Roots
For exampe, let’s simplify square root of 75. To do this, remove all full squares inside the square root.
- Factorize the number: 75 = 5 * 5 * 3 = 25 * 3.
- Using the square root rule \sqrt{ab} = \sqrt{a} * \sqrt{b}, we get \sqrt{75} = \sqrt{25 * 3} = \sqrt{25} * \sqrt{3} = 5\sqrt{3}
Simplify square root of 72.
72 = 6 * 6 * 2 = 36 * 2
\sqrt{72} = \sqrt{36 * 2} = \sqrt{36} * \sqrt{2} = 6\sqrt{2} \approx{8.48528}
Simplify the square root of 48.
48 = 16 * 3
\sqrt{48} = \sqrt{16 * 3} = \sqrt{16} * \sqrt{3} = 4\sqrt{3} \approx{6.9282}
List of perfect squares
List of Perfect Squares. The first 100 perfect squares are listed below
1 = 1 * 1 = 12 | 2601 = 51 * 51 = 512 |
4 = 2 * 2 = 22 | 2704 = 52 * 52 = 522 |
9 = 3 * 3 = 32 | 2809 = 53 * 53 = 532 |
16 = 4 * 4 = 42 | 2916 = 54 * 54 = 542 |
25 = 5 * 5 = 52 | 3025 = 55 * 55 = 552 |
36 = 6 * 6 = 62 | 3136 = 56 * 56 = 562 |
49 = 7 * 7 = 72 | 3249 = 57 * 57 = 572 |
64 = 8 * 8 = 82 | 3364 = 58 * 58 = 582 |
81 = 9 * 9 = 92 | 3481 = 59 * 59 = 592 |
100 = 10 * 10 = 102 | 3600 = 60 * 60 = 602 |
121 = 11 * 11 = 112 | 3721 = 61 * 61 = 612 |
144 = 12 * 12 = 122 | 3844 = 62 * 62 = 622 |
169 = 13 * 13 = 132 | 3969 = 63 * 63 = 632 |
196 = 14 * 14 = 142 | 4096 = 64 * 64 = 642 |
225 = 15 * 15 = 152 | 4225 = 65 * 65 = 652 |
256 = 16 * 16 = 162 | 4356 = 66 * 66 = 662 |
289 = 17 * 17 = 172 | 4489 = 67 * 67 = 672 |
324 = 18 * 18 = 182 | 4624 = 68 * 68 = 682 |
361 = 19 * 19 = 192 | 4761 = 69 * 69 = 692 |
400 = 20 * 20 = 202 | 4900 = 70 * 70 = 702 |
441 = 21 * 21 = 212 | 5041 = 71 * 71 = 712 |
484 = 22 * 22 = 222 | 5184 = 72 * 72 = 722 |
529 = 23 * 23 = 232 | 5329 = 73 * 73 = 732 |
576 = 24 * 24 = 242 | 5476 = 74 * 74 = 742 |
625 = 25 * 25 = 252 | 5625 = 75 * 75 = 752 |
676 = 26 * 26 = 262 | 5776 = 76 * 76 = 762 |
729 = 27 * 27 = 272 | 5929 = 77 * 77 = 772 |
784 = 28 * 28 = 282 | 6084 = 78 * 78 = 782 |
841 = 29 * 29 = 292 | 6241 = 79 * 79 = 792 |
900 = 30 * 30 = 302 | 6400 = 80 * 80 = 802 |
961 = 31 * 31 = 312 | 6561 = 81 * 81 = 812 |
1024 = 32 * 32 = 322 | 6724 = 82 * 82 = 822 |
1089 = 33 * 33 = 332 | 6889 = 83 * 83 = 832 |
1156 = 34 * 34 = 342 | 7056 = 84 * 84 = 842 |
1225 = 35 * 35 = 352 | 7225 = 85 * 85 = 852 |
1296 = 36 * 36 = 362 | 7396 = 86 * 86 = 862 |
1369 = 37 * 37 = 372 | 7569 = 87 * 87 = 872 |
1444 = 38 * 38 = 382 | 7744 = 88 * 88 = 882 |
1521 = 39 * 39 = 392 | 7921 = 89 * 89 = 892 |
1600 = 40 * 40 = 402 | 8100 = 90 * 90 = 902 |
1681 = 41 * 41 = 412 | 8281 = 91 * 91 = 912 |
1764 = 42 * 42 = 422 | 8464 = 92 * 92 = 922 |
1849 = 43 * 43 = 432 | 8649 = 93 * 93 = 932 |
1936 = 44 * 44 = 442 | 8836 = 94 * 94 = 942 |
2025 = 45 * 45 = 452 | 9025 = 95 * 95 = 952 |
2116 = 46 * 46 = 462 | 9216 = 96 * 96 = 962 |
2209 = 47 * 47 = 472 | 9409 = 97 * 97 = 972 |
2304 = 48 * 48 = 482 | 9604 = 98 * 98 = 982 |
2401 = 49 * 49 = 492 | 9801 = 99 * 99 = 992 |
2500 = 50 * 50 = 502 | 10000 = 100 * 100 = 1002 |
Example Square Roots
- Square roots of 16 is 4, because 42 = 16
- Square roots of 121 is 11, because 112 = 121
- Square roots of 196 is 14, because 142 = 196
- Square roots of 256 is 16, because 162 = 256
- Square roots of 289 is 17, because 172 = 286
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