Square & Cube Root Calculator
The square root of a number x is a value r such that r² = x. More generally, the nth root of x is the value r satisfying rⁿ = x, computed as x^(1/n). This calculator instantly finds the square root, cube root, and any custom nth root of any real number, and automatically detects whether the result is a perfect square, perfect cube, or perfect power.
Negative numbers have no real square root (or any even-degree root), but do have real cube roots and other odd-degree roots. Enter your number and optionally adjust the root degree to explore all three results side by side. Perfect-square and perfect-cube badges highlight exact integer results.
How it works
ⁿ√x = x^(1/n). Square root: √x = x^(1/2). Cube root: ∛x = x^(1/3). For negative x and even n, the result is not real. A number x is a perfect nth power when x^(1/n) is an integer.
Use cases
- Finding the side length of a square given its area
- Solving quadratic and higher-degree polynomial equations
- Computing standard deviation in statistics (involves square roots)
- Determining the edge length of a cube given its volume
- Simplifying radical expressions in algebra homework