# 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.

### Inputs

### N^{th }Roots

The application of this calculator is to determine the n^{th} root of a given number, *x*. This can be useful when performing general calculations in designing a system, circuit, and many other situations. The n^{th} 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 n^{th} 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.

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