Simplify square roots (radicals) that have fractions

We will look at some examples of simplifying fractions within a square root (or radical).

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

Example :

For any positive number x and y,

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

Example :

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

Example :

Example:

Calculate the value of the following:

Solution:

The following video shows how to simplify fractions inside a square root.

The following shows how to simplify square roots in the denominator of a fraction.

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