# 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.

## 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 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

1. $$\color{blue}{\frac{1}{\sqrt{6}}}$$
2. $$\color{blue}{\frac{5}{\sqrt{3}}}$$
3. $$\color{blue}{\frac{3}{\sqrt{7}-1}}$$
4. $$\color{blue}{\frac{8}{\sqrt{5}+3}}$$
1. $$\color{blue}{\frac{\sqrt{6}}{6}}$$
2. $$\color{blue}{\frac{5\sqrt{3}}{3}}$$
3. $$\color{blue}{\frac{\sqrt{7}+1}{2}}$$
4. $$\color{blue}{-2\sqrt{5}+6}$$

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