This root calculator finds the square root, cube root or any nth root of a number. As well as the decimal answer, it gives the simplified radical form, such as √72 = 6√2, and says whether the number is a perfect square or cube.
What is a root?
The nth root of x is the number that, multiplied by itself n times, gives x. The square root of 49 is 7 because 7 × 7 = 49, and the cube root of 125 is 5 because 5 × 5 × 5 = 125. In exponent form, the nth root of x is x1/n.
How to simplify a radical
- Find the largest perfect square (or cube, for cube roots) that divides the number.
- Take its root outside the radical sign.
- Leave the rest inside.
Example: 72 = 36 × 2, so √72 = √36 × √2 = 6√2 ≈ 8.4853. For a cube root, 54 = 27 × 2, so ∛54 = 3∛2.
Perfect squares and cubes
| n | n² | n³ |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1,000 |
| 11 | 121 | 1,331 |
| 12 | 144 | 1,728 |
Roots of negative numbers
Odd roots of negative numbers are real: ∛−8 = −2. Even roots of negative numbers are not real numbers; √−16 = 4i, where i is the imaginary unit √−1.
Frequently asked questions
What is the square root of 2?
About 1.41421356. It is irrational, so its decimals never end or repeat.
Does a number have two square roots?
Yes: both 5 and −5 square to 25. The √ symbol means the positive (principal) root.
How do I find a root without a calculator?
Estimate between two perfect powers, then refine. For example, √50 is just over 7, since 7² = 49.
What is a 4th root?
The number that multiplied by itself four times gives x. The 4th root of 81 is 3.
Related calculators
Last reviewed: October 2026. For information only; results are estimates; check important figures with a professional.