Square Root, Cube Root, and Nth Root Calculator

This calculator will determine the square root, cube root, or nth root of a given number, x.


Nth Roots

The application of this calculator is to determine the nth root of a given number, x. This can be useful when performing general calculations in designing a system, circuit, and many other situations. The nth root of x is defined as a number y raised to the power n that equals x.


$$x = y^{n}$$


It can also be thought of as y multiplied by itself n times:


$$x = y \cdot y \cdot \ldots \cdot y$$, n times


This nth root of x is represented mathematically using the radical symbol:


$$y = \sqrt[n]{x}$$


Where the positive integer value n is called the index of the radical.


Square Roots

The square root is a special case where the index of the radical is two.

Square roots are the most commonly calculated root functions:


$$y = \sqrt[2]{x}$$


Cube Roots

Cube roots have an index of three and are also common:


$$y = \sqrt[3]{x}$$

For negative values of x, the nth root is undefined if n is an even integer since we are assuming only real numbers in these calculations.


Further Reading