Root Calculator
Calculate square roots, cube roots and any n-th root, with perfect-root detection.
Last updated: August 2026
2 = square root, 3 = cube root, etc.
Root
12
2nd root of 144
Perfect root?
Perfect
Exact value 12
Check
144
Root raised to the power 2
A perfect root is one where the answer is an exact integer, such as the square root of 144 being 12. Even-indexed roots of negative numbers are not defined here.
How it works
n-th root = value^(1/n). A perfect root is an exact integer.
Example: √144 = 12 (perfect); √2 ≈ 1.4142 (not perfect).
Frequently Asked Questions
What is a square root?
The square root of a number is the value that, multiplied by itself, gives the original number. The square root of 144 is 12 because 12 × 12 = 144.
What is an n-th root?
The n-th root of a number is the value that, raised to the power of n, gives the original number. The cube root of 27 is 3 because 3 × 3 × 3 = 27.
What is the square root of a negative number?
Negative numbers do not have real square roots — the answer is imaginary (i times the root of the absolute value). The calculator only returns real roots.
What is the difference between a square root and a cube root?
A square root is the value that squares to the number; a cube root is the value that cubes to it. The square root of 8 is about 2.83, but the cube root of 8 is exactly 2.