Square Roots of 1 to 100 and the Perfect Squares
The square root of a number is the value that multiplies by itself to give it. The table lists every square root from 1 to 100 and the perfect squares up to 400, as a decimal and in simplified radical form. Open any number for the step-by-step simplification.
How to read the table
- A perfect square has a whole-number root, so its decimal is exact. The perfect squares here are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400.
- Every other number has an irrational root: the decimal never ends or repeats, so the table rounds it to four places.
- Simplified form pulls the largest perfect square out from under the radical. For example, 72 equals 36 times 2, so the square root of 72 is 6√2. Numbers with no perfect-square factor larger than 1, such as 7 or 10, are already in simplest form.
| Number | Square root (4 places) | Simplified | Type |
|---|---|---|---|
| Square root of 1 | 1 | 1 | Perfect square |
| Square root of 2 | 1.4142 | √2 | Already simplest |
| Square root of 3 | 1.7321 | √3 | Already simplest |
| Square root of 4 | 2 | 2 | Perfect square |
| Square root of 5 | 2.2361 | √5 | Already simplest |
| Square root of 6 | 2.4495 | √6 | Already simplest |
| Square root of 7 | 2.6458 | √7 | Already simplest |
| Square root of 8 | 2.8284 | 2√2 | Simplifies |
| Square root of 9 | 3 | 3 | Perfect square |
| Square root of 10 | 3.1623 | √10 | Already simplest |
| Square root of 11 | 3.3166 | √11 | Already simplest |
| Square root of 12 | 3.4641 | 2√3 | Simplifies |
| Square root of 13 | 3.6056 | √13 | Already simplest |
| Square root of 14 | 3.7417 | √14 | Already simplest |
| Square root of 15 | 3.873 | √15 | Already simplest |
| Square root of 16 | 4 | 4 | Perfect square |
| Square root of 17 | 4.1231 | √17 | Already simplest |
| Square root of 18 | 4.2426 | 3√2 | Simplifies |
| Square root of 19 | 4.3589 | √19 | Already simplest |
| Square root of 20 | 4.4721 | 2√5 | Simplifies |
| Square root of 21 | 4.5826 | √21 | Already simplest |
| Square root of 22 | 4.6904 | √22 | Already simplest |
| Square root of 23 | 4.7958 | √23 | Already simplest |
| Square root of 24 | 4.899 | 2√6 | Simplifies |
| Square root of 25 | 5 | 5 | Perfect square |
| Square root of 26 | 5.099 | √26 | Already simplest |
| Square root of 27 | 5.1962 | 3√3 | Simplifies |
| Square root of 28 | 5.2915 | 2√7 | Simplifies |
| Square root of 29 | 5.3852 | √29 | Already simplest |
| Square root of 30 | 5.4772 | √30 | Already simplest |
| Square root of 31 | 5.5678 | √31 | Already simplest |
| Square root of 32 | 5.6569 | 4√2 | Simplifies |
| Square root of 33 | 5.7446 | √33 | Already simplest |
| Square root of 34 | 5.831 | √34 | Already simplest |
| Square root of 35 | 5.9161 | √35 | Already simplest |
| Square root of 36 | 6 | 6 | Perfect square |
| Square root of 37 | 6.0828 | √37 | Already simplest |
| Square root of 38 | 6.1644 | √38 | Already simplest |
| Square root of 39 | 6.245 | √39 | Already simplest |
| Square root of 40 | 6.3246 | 2√10 | Simplifies |
| Square root of 41 | 6.4031 | √41 | Already simplest |
| Square root of 42 | 6.4807 | √42 | Already simplest |
| Square root of 43 | 6.5574 | √43 | Already simplest |
| Square root of 44 | 6.6332 | 2√11 | Simplifies |
| Square root of 45 | 6.7082 | 3√5 | Simplifies |
| Square root of 46 | 6.7823 | √46 | Already simplest |
| Square root of 47 | 6.8557 | √47 | Already simplest |
| Square root of 48 | 6.9282 | 4√3 | Simplifies |
| Square root of 49 | 7 | 7 | Perfect square |
| Square root of 50 | 7.0711 | 5√2 | Simplifies |
| Square root of 51 | 7.1414 | √51 | Already simplest |
| Square root of 52 | 7.2111 | 2√13 | Simplifies |
| Square root of 53 | 7.2801 | √53 | Already simplest |
| Square root of 54 | 7.3485 | 3√6 | Simplifies |
| Square root of 55 | 7.4162 | √55 | Already simplest |
| Square root of 56 | 7.4833 | 2√14 | Simplifies |
| Square root of 57 | 7.5498 | √57 | Already simplest |
| Square root of 58 | 7.6158 | √58 | Already simplest |
| Square root of 59 | 7.6811 | √59 | Already simplest |
| Square root of 60 | 7.746 | 2√15 | Simplifies |
| Square root of 61 | 7.8102 | √61 | Already simplest |
| Square root of 62 | 7.874 | √62 | Already simplest |
| Square root of 63 | 7.9373 | 3√7 | Simplifies |
| Square root of 64 | 8 | 8 | Perfect square |
| Square root of 65 | 8.0623 | √65 | Already simplest |
| Square root of 66 | 8.124 | √66 | Already simplest |
| Square root of 67 | 8.1854 | √67 | Already simplest |
| Square root of 68 | 8.2462 | 2√17 | Simplifies |
| Square root of 69 | 8.3066 | √69 | Already simplest |
| Square root of 70 | 8.3666 | √70 | Already simplest |
| Square root of 71 | 8.4261 | √71 | Already simplest |
| Square root of 72 | 8.4853 | 6√2 | Simplifies |
| Square root of 73 | 8.544 | √73 | Already simplest |
| Square root of 74 | 8.6023 | √74 | Already simplest |
| Square root of 75 | 8.6603 | 5√3 | Simplifies |
| Square root of 76 | 8.7178 | 2√19 | Simplifies |
| Square root of 77 | 8.775 | √77 | Already simplest |
| Square root of 78 | 8.8318 | √78 | Already simplest |
| Square root of 79 | 8.8882 | √79 | Already simplest |
| Square root of 80 | 8.9443 | 4√5 | Simplifies |
| Square root of 81 | 9 | 9 | Perfect square |
| Square root of 82 | 9.0554 | √82 | Already simplest |
| Square root of 83 | 9.1104 | √83 | Already simplest |
| Square root of 84 | 9.1652 | 2√21 | Simplifies |
| Square root of 85 | 9.2195 | √85 | Already simplest |
| Square root of 86 | 9.2736 | √86 | Already simplest |
| Square root of 87 | 9.3274 | √87 | Already simplest |
| Square root of 88 | 9.3808 | 2√22 | Simplifies |
| Square root of 89 | 9.434 | √89 | Already simplest |
| Square root of 90 | 9.4868 | 3√10 | Simplifies |
| Square root of 91 | 9.5394 | √91 | Already simplest |
| Square root of 92 | 9.5917 | 2√23 | Simplifies |
| Square root of 93 | 9.6437 | √93 | Already simplest |
| Square root of 94 | 9.6954 | √94 | Already simplest |
| Square root of 95 | 9.7468 | √95 | Already simplest |
| Square root of 96 | 9.798 | 4√6 | Simplifies |
| Square root of 97 | 9.8489 | √97 | Already simplest |
| Square root of 98 | 9.8995 | 7√2 | Simplifies |
| Square root of 99 | 9.9499 | 3√11 | Simplifies |
| Square root of 100 | 10 | 10 | Perfect square |
| Square root of 121 | 11 | 11 | Perfect square |
| Square root of 144 | 12 | 12 | Perfect square |
| Square root of 169 | 13 | 13 | Perfect square |
| Square root of 196 | 14 | 14 | Perfect square |
| Square root of 225 | 15 | 15 | Perfect square |
| Square root of 256 | 16 | 16 | Perfect square |
| Square root of 289 | 17 | 17 | Perfect square |
| Square root of 324 | 18 | 18 | Perfect square |
| Square root of 361 | 19 | 19 | Perfect square |
| Square root of 400 | 20 | 20 | Perfect square |
Need a different number?
The square root calculator works for any number and shows the simplification steps. A number's factors reveal whether it is a perfect square, and the Roman numerals table covers the same 1 to 100 range.