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Table of contents:

  1. Square Root Calculator
  2. What is a Square Root?
  3. Perfect Square Calculator
  4. Simplify Square Roots
  5. List of Perfect Squares
  6. Example Square Roots

What is a Square Root?

In mathematics, a square root of a number x is a number y such that y2 = x

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.

The square root is denoted by the symbol √

For example, square root of 9 denoted as √9.

Perfect Square Calculator

A perfect square is an integer that is the product of some integer with itself.

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.

  1. Factorize the number: 75 = 5 * 5 * 3 = 25 * 3.
  2. 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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