Simplifying The Square Root Of A Fraction

There are two different methods for simplifying the square root of a fraction. First there is the case where the nominator and the denominator have perfect root. Forexample,

From this set, we can conclude that the square root of a fraction is equal to the square of the numerator divided by the square root of the denominator. Example:

But, there a second case for simplifying the square root of a fraction whose denominator is not a perfect square. For this type of problem, some procedure must be followed:

1) Change the fraction to an equivalent fraction

2) Denominator must have the smallest perfect square.

3) Simplify the perfect square whenever it is possible.

Example 1

Simplify the square roots of the following fractions.

1) √2/3

Solution

a) Change to an equivalent fraction

√2/3.3/3 = √6/9

b) But, √6/9 is equal to √6/√9

c) Thus, √6/√9 = √6/3

Example 2

√1/5

Solution

a) Change to equivalent fraction

√1/5 . 5/5 = √5/25

b) But, √5/25 is equal to √5/√25

c) Thus, √5/√25 = √5/5

Example 3

√3/8

Solution

a) Change to equivalent fraction

√3/8. 2/2 = √6/16

b) But, √(6/16) = √6/√16

c) Thus,√6/√16 = √6/4