How to Simplify Radical Expressions Involving Fractions?

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

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.

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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

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. \(\color{blue}{\frac{8}{\sqrt{5}+3}}\)
This image has an empty alt attribute; its file name is answers.png
  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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