About the root calculator
The nth root of x is the number that, multiplied by itself n times, gives x. The square root is n = 2 and the cube root is n = 3. Enter a number and the root index to see the answer to many decimal places.
When the number is a whole number, the calculator also simplifies the radical: the square root of 72 is 6√2, because 72 = 36 × 2.
Odd roots of negative numbers are fine: the cube root of −27 is −3. Even roots of negative numbers are not real numbers, so the principal complex value is shown instead, such as √−4 = 2i.
Formula
- ⁿ√x = x^(1/n)
- √(a × b) = √a × √b
- Even roots need x ≥ 0 for a real result
- Odd roots are defined for all real x
Example
√144 = 12. The cube root of −27 is −3. The fourth root of 81 is 3. √72 = 6√2 ≈ 8.485.