# How to Simplify Radical Expressions Involving Fractions?

To simplify radical expressions involving fractions, we have two simple methods.

A radical contains an expression that is not a perfect root it is called an irrational number. To rationalize the denominator, you need to get rid of all radicals that are in the denominator.

## Related Topics

- How to Rationalize Radical Expressions
- How to Simplify Radical Expressions
- How to Multiply Radical Expressions

## Step by Step Guide to Simplifying Radical Expressions Involving Fraction

To simplify radical expressions involving fractions:

- If there is a radical in the denominator, multiply the numerator and denominator by the radical in the denominator.
- If there is a radical and another integer in the denominator, multiply both the numerator and denominator by the conjugate of the denominator.

**Simplifying Radical Expressions Involving Fractions** **– Example 1:**

Simplify. \(\frac{1}{\sqrt{7}}\)

**Solution:**

Multiply by the \(\sqrt{7}\): \(\frac{1}{\sqrt{7}} × \frac{\sqrt{7}}{\sqrt{7}}= \frac{\sqrt{7}} {7}\)

**Simplifying Radical Expressions Involving Fractions** **– Example 2:**

Simplify. \(\frac{2}{\sqrt{3}+1}\)

**Solution:**

Multiply by the conjugate: \(\frac{\sqrt{3}-1} {\sqrt{3}-1}\)

\(\frac{2}{\sqrt{3}+1} × \frac{\sqrt{3}-1} {\sqrt{3}-1}=\frac{2(\sqrt{3}-1)}{2}=\sqrt{3}-1\)

## Exercises for Simplifying Radical Expressions Involving Fractions

### Simplify radical expressions.

- \(\color{blue}{\frac{1}{\sqrt{6}}}\)
- \(\color{blue}{\frac{5}{\sqrt{3}}}\)
- \(\color{blue}{\frac{3}{\sqrt{7}-1}}\)
- \(\color{blue}{\frac{8}{\sqrt{5}+3}}\)

- \(\color{blue}{\frac{\sqrt{6}}{6}}\)
- \(\color{blue}{\frac{5\sqrt{3}}{3}}\)
- \(\color{blue}{\frac{\sqrt{7}+1}{2}}\)
- \(\color{blue}{-2\sqrt{5}+6}\)

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