How to Simplify Radical Expressions Involving Fractions?

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

A 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.

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. \(\color{blue}{-2\sqrt{5}+6}\)