The square root of a number is the value that, multiplied by itself, gives that number: √49 = 7 because 7 × 7 = 49. This calculator also gives the cube root, any n-th root, the simplest radical form used in school maths, and tells you if the number is a perfect square.
How to use the square root calculator
- Enter the number.
- Optionally, change n to see another root, such as the 4th or 5th root.
Simplest radical form
Split the number into a perfect square times the rest, and take the square root of the perfect square outside:
√50 = √(25 × 2) = 5√2
√72 = √(36 × 2) = 6√2
√12 = √(4 × 3) = 2√3Example
For 50:
- Square root: 7.071068
- Simplest form: 5√2
- Cube root: 3.684031
- 4th root: 2.659148
- 50 is not a perfect square; it lies between 7² = 49 and 8² = 64.
Perfect squares up to 20²
| n | n² | n | n² |
|---|---|---|---|
| 1 | 1 | 11 | 121 |
| 2 | 4 | 12 | 144 |
| 3 | 9 | 13 | 169 |
| 4 | 16 | 14 | 196 |
| 5 | 25 | 15 | 225 |
| 6 | 36 | 16 | 256 |
| 7 | 49 | 17 | 289 |
| 8 | 64 | 18 | 324 |
| 9 | 81 | 19 | 361 |
| 10 | 100 | 20 | 400 |
FAQ
Can a negative number have a square root?
Not among real numbers, because any real number times itself is positive or zero. Cube roots of negative numbers do exist: ∛−27 = −3.
How do I estimate a square root without a calculator?
Find the perfect squares around it. √50 is a little more than √49 = 7, so about 7.07.
What is the square root of 2?
About 1.414214. It never ends or repeats, so it is an irrational number.