# Radicals

A** radical** is an expression of the type , where **n** is the index and **a** is the radicand.

A **radical** can also be expressed in the form of** a power: **

### Simplifying Radicals

1 If an exponent is lower than the index, the factor is left in the radicand

2 If an exponent is equal to the index, the factor goes outside the radicand.

3 If an exponent is greater than the index and is divided by the index, the quotient is the exponent of the factor outside the radicand and the remainder is the exponent of the factor within the radicand.

The inverse operation can also be performed.

### Addition and Subtraction of Radicals

Two radicals can only be added (or subtracted) when they have the same index and radicand, that is to say, they are **similar radicals**.

#### Example

### Multiplication of Radicals

#### Same Index

To multiply radicals with the same index, multiply the radicands and the index remains the same.

#### Different Index

First, reduce to a common index and then multiply.

1.The common index is the least common multiple of the indices.

2.Divide the common index by each of the indices and each result is multiplied by their corresponding exponents.

#### Examples

### Division of Radicals

#### Same Index

To divide radicals with the same index, divide the radicands and the same index is used for the resultant radicand.

#### Different Index

Reduce to a common index and divide.

#### Examples