Squares and square roots table
The squares and square roots of the numbers 1 through 30. Squaring multiplies a number by itself; the square root is the reverse, the value that squares back to the number. Perfect squares have whole-number roots.
Squares and square roots (1 to 30)
| n | n² (square) | √n (square root) |
|---|---|---|
| 1 | 1 | 1.0000 |
| 2 | 4 | 1.4142 |
| 3 | 9 | 1.7321 |
| 4 | 16 | 2.0000 |
| 5 | 25 | 2.2361 |
| 6 | 36 | 2.4495 |
| 7 | 49 | 2.6458 |
| 8 | 64 | 2.8284 |
| 9 | 81 | 3.0000 |
| 10 | 100 | 3.1623 |
| 11 | 121 | 3.3166 |
| 12 | 144 | 3.4641 |
| 13 | 169 | 3.6056 |
| 14 | 196 | 3.7417 |
| 15 | 225 | 3.8730 |
| 16 | 256 | 4.0000 |
| 17 | 289 | 4.1231 |
| 18 | 324 | 4.2426 |
| 19 | 361 | 4.3589 |
| 20 | 400 | 4.4721 |
| 21 | 441 | 4.5826 |
| 22 | 484 | 4.6904 |
| 23 | 529 | 4.7958 |
| 24 | 576 | 4.8990 |
| 25 | 625 | 5.0000 |
| 26 | 676 | 5.0990 |
| 27 | 729 | 5.1962 |
| 28 | 784 | 5.2915 |
| 29 | 841 | 5.3852 |
| 30 | 900 | 5.4772 |
A perfect square is a number whose square root is a whole number, such as 1, 4, 9, 16, and 25. For numbers in between, the square root is irrational and runs on without repeating, so the values here are rounded to four decimal places.
Need cubes too?
See the Cubes and Cube Roots Table.
Squares and square roots
To square a number, multiply it by itself: 6 squared is 6 times 6, which is 36. The square root undoes this, so the square root of 36 is 6. Every positive number has a square root, but only perfect squares have whole-number roots; the rest are irrational decimals that never terminate or repeat.
Estimating a square root
To estimate a root that is not perfect, find the nearest perfect squares on either side. The square root of 50 lies between 7 (root of 49) and 8 (root of 64), much closer to 7, so it is about 7.07. This bracketing trick gives a quick mental approximation without a calculator.
FAQ
What is a perfect square?
A number whose square root is a whole number, such as 25 (root 5) or 81 (root 9).
What is the square root of 2?
About 1.4142. It is an irrational number, so its decimal continues forever without repeating.
How do I find a square root without a calculator?
Bracket it between the nearest perfect squares. The root of 30 is between 5 and 6, closer to 5.5, since 30 sits between 25 and 36.