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:

Pre-Algebra for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

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