# Simplifying Radicals

### by Mei Bibian

## Vocabulary

Factor Tree: a tool that breaks down any number into its prime factors

Exponent: a quantity representing the power to which a given number or expression is to be raised

Factor: a number or quantity that when multiplied with another produces a given number or expression

## Example

To simplify start by making a factor tree for the number inside the root. Now look for pairs of factors that are the same. If the factor pairs up then it will come out of the radical. If the factor does not pair up then it stays inside of the radical. If you have any number that can't pair up, leave it in the radical.

√98

/ \

2*49

49

/ \

7*7

= 7√2

Same for cube roots. Instead of having pairs have the factors in sets of 3s.

## Example with Exponents

When you have a variable with an exponent in your radical do the same as if it were a factor.

√2x^7

x^7

/ \

x*x*x*x*x*x*x

So now we have 3 pairs of x's and they go out of the root.

x^3√2x