# Radicals

A** radical** is an expression denoted as , in which **n** and **a**; so that when **a** is negative, n must be odd.

#### Powers and Radicals

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

### Equivalent Radicals

Using the notation of a fractional exponent and the property which says that if you multiply the numerator and denominator by the same number, the fraction is equivalent and the following is obtained:

If you multiply or divide the index and the exponent of a** radical** by the same** natural number**, obtained is another** equivalent radical. **

### Simplifying Radicals

If there is a** natural number** that divides the** index** and the exponent (or the exponents) of a radicand, you get a** simplified radical**.

### Common Index

1The 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**.

### Extraction of Factors

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.