Simplify Squares Roots (Radicals) That Have Fractions

Related Pages

• Square Root Worksheets

  Printable
  Squares & Cubes (whole number, fraction & decimal bases)
  Squares & square roots
  Cubes & cube roots
  

  Simplify square roots
  Rationalize denominators
  

How to find the square root of a fraction?

The following are some of the steps that can be used to find the square root of a fraction:

Separate Numerator & Denominator

A. The square root of some fractions can be determined by finding the square root of the numerator and denominator separately.

Example:
\(\sqrt {\frac{{16}}{{25}}} = \frac{{\sqrt {16} }}{{\sqrt {25} }} = \frac{{\sqrt {{4^2}} }}{{\sqrt {{5^2}} }} = \frac{4}{5}\)

For any positive number x and y,
\(\sqrt {\frac{x}{y}} = \frac{{\sqrt x }}{{\sqrt y }}\)

In other words, the square root of a fraction is a fraction of square roots.

Reduce Fraction

B. Some fractions can be reduced to fractions with perfect squares as the numerator and denominator. Then, the square root of the simplified fraction can be determined as shown in the example below.

Example:
\(\sqrt {\frac{{18}}{{50}}} = \sqrt {\frac{9}{{25}}} = \frac{{\sqrt {{3^2}} }}{{\sqrt {{5^2}} }} = \frac{3}{5}\)

Change to Improper Fraction

C. For a mixed number, change it to an improper fraction before finding the square root.

Example:
\(\sqrt {1\frac{{13}}{{36}}} = \sqrt {\frac{{49}}{{36}}} = \frac{{\sqrt {{7^2}} }}{{\sqrt {{6^2}} }} = \frac{7}{6} = 1\frac{1}{6}\)

Example:
Calculate the value of each of the following:
\(\begin{array}{l}{\rm{a)}}\,\,\sqrt {\frac{{25}}{{36}}} \\{\rm{b)}}\,\,\sqrt {\frac{{18}}{{32}}} \\{\rm{c)}}\,\,\sqrt {1\frac{{11}}{{25}}} \end{array}\)

Solution:

Simplify Square Root Worksheets
Simplify square roots
Rationalize denominators

How to simplify fractions inside a square root?

• Show Video Lesson

How to simplify square roots in the denominator of a fraction?

• Show Video Lesson

Square Roots of Fractions/Rational Numbers

Finding the square of rational numbers for perfect squares as well as estimating non-perfect squares.

• Show Video Lesson

Quotient Rule & Simplifying Square Roots

An introduction to the quotient rule for square roots and radicals and how to use it to simplify expressions containing radicals.

• Show Video Lesson

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.