Square Root Calculator
Find the square root and cube root of any number, with the simplest radical form for whole numbers.
What a square root is
The square root of x is the number that, multiplied by itself, gives x. √81 = 9 because 9 × 9 = 81. Every positive number has two square roots (9 and −9); the √ symbol means the positive one.
Simplifying radicals
To simplify a square root, factor out the largest perfect square. 72 = 36 × 2, so √72 = √36 × √2 = 6√2 ≈ 8.485.
Perfect squares to memorize
| n | n² | n | n² |
|---|---|---|---|
| 1 | 1 | 9 | 81 |
| 2 | 4 | 10 | 100 |
| 3 | 9 | 11 | 121 |
| 4 | 16 | 12 | 144 |
| 5 | 25 | 13 | 169 |
| 6 | 36 | 14 | 196 |
| 7 | 49 | 15 | 225 |
| 8 | 64 | 20 | 400 |
Estimating without a calculator
Find the perfect squares on either side. √50 lies between √49 = 7 and √64 = 8, much closer to 7: about 7.07. Square roots of negative numbers are imaginary: √−16 = 4i.
Frequently asked questions
What is the square root of 2?
About 1.41421356. It is irrational, so its decimal never ends or repeats.
How do I simplify √50?
50 = 25 × 2, so √50 = 5√2.
What is a cube root?
The number that multiplied by itself three times gives x. The cube root of 27 is 3.
Last reviewed October 2026. Results are estimates; check important decisions with a qualified professional.