# Root

The term "root" has a few different meanings in the context of algebra. One meaning of a root is as the solution to a radical expression. Another is as the values for which a polynomial evaluates to 0.

## Radical expressions/n^{th} roots

For the first meaning of root mentioned above, given a radical expression, such as

the root of x, indicated above as "z," is the value, that when multiplied by itself a given number of times, equals x. The number of times that x needs to be multiplied by itself is given by n, so we use the term "n^{th} root." The most commonly used roots are the square root (n = 2) and the cubed root (n = 3), though n can be any number.

Examples

1. Evaluate :

We can read this problem as "what value, raised to the power of 2, equals 144?" 144 is a perfect square (12^{2}), so:

In this example, 12 is the root.

2. Evaluate :

We solve this in the same way as we do example 1, by finding the value, that raised to the power of 3, equals 64. 64 is a perfect cube (4^{3}), so:

In this example, 4 is the root.

## Roots of polynomials

Solving polynomials involves setting the polynomial equal to 0, and finding the value(s) for which the polynomial is equal to 0. These values, or the solutions, are called roots.

Examples

Find the roots of the following expressions.

1.

In this example, the roots are 3 and -3.

2.

In this example, the roots are 2 and -2.

3.

In this example, the root is -1