## 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.