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