 # Square Root of Number in the Fraction Form | Simplifying Square Roots of Fractions Examples

Square Root of Number in the Fraction Form is explained clearly in this article. Finding natural numbers is easy but when it comes to fractions it is a little bit difficult to find the Square Root of Numbers. So, to make the process easy, we have given the step by step procedure on How do you find the Square Root of a Fraction. Check all the sample problems on finding the square root of numbers in fraction form and get to know the concept involved.

## How to Find the Square Root of a Fraction?

If m and n are squares of some numbers then, √(m ÷ n) = √m ÷ √n. If you find any problem in mixed form, then convert it into fractions.

1. Find the square root of √(144 ÷ 81)?

Solution:
Given the number is √(144 ÷ 81).
Firstly, separate the numerator and denominator.
√(144) ÷ √(81)
Find the separate Square Roots of the numerator and denominator.
Find the prime factors of √(144)
√(144) = 12 × 12
Grouping the factors into the pairs of equal factors.
(12 × 12)
Take one number from each group and multiply them to find the number whose square is 144.
12
The square root of 144 is 12.
Find the prime factors of √(81)
√(81) = 9 × 9
Grouping the factors into the pairs of equal factors.
(9 × 9)
Take one number from each group and multiply them to find the number whose square is 81.
9.
The square root of 81 is 9.
The final answer is 12 ÷ 9 = 4/3

Therefore, the square root of √(144 ÷ 81) = 4/3.

2. Evaluate √(256 ÷ 64)?

Solution:
Given the number is √(256 ÷ 64).
Firstly, separate the numerator and denominator.
√(256) ÷ √(64)
Find the separate Square Roots of the numerator and denominator.
Find the prime factors of √(256)
√(256) = 16 × 16
Grouping the factors into the pairs of equal factors.
(16 × 16)
Take one number from each group and multiply them to find the number whose square is 256.
16
The square root of 256 is 16.
Find the prime factors of √(64)
√(64) = 8 × 8
Grouping the factors into the pairs of equal factors.
(8 × 8)
Take one number from each group and multiply them to find the number whose square is 64.
8.
The square root of 64 is 8.
The final answer is 256 ÷ 64 = 16/8

Therefore, the square root of √(256 ÷ 64) = 16/8.

3. Evaluate √(49 ÷ 121)?

Solution:
Given the number is √(49 ÷ 121).
Firstly, separate the numerator and denominator.
√(49) ÷ √(121)
Find the separate Square Roots of the numerator and denominator.
Find the prime factors of √(49)
√(49) = 7 × 7
Grouping the factors into the pairs of equal factors.
(7 × 7)
Take one number from each group and multiply them to find the number whose square is 49.
7
The square root of 49 is 7.
Find the prime factors of √(121)
√(121) = 11 × 11
Grouping the factors into the pairs of equal factors.
(11 × 11)
Take one number from each group and multiply them to find the number whose square is 121.
11.
The square root of 121 is 11.
The final answer is 49 ÷ 121 = 7/11

Therefore, the square root of √(49 ÷ 121) = 7/11.

4. Evaluate √(25 ÷ 169)?

Solution:
Given the number is √(25 ÷ 169).
Firstly, separate the numerator and denominator.
√(25) ÷ √(169)
Find the separate Square Roots of the numerator and denominator.
Find the prime factors of √(25)
√(25) = 5 × 5
Grouping the factors into the pairs of equal factors.
(5 × 5)
Take one number from each group and multiply them to find the number whose square is 25.
5
The square root of 25 is 5.
Find the prime factors of √(169)
√(169) = 13 × 13
Grouping the factors into the pairs of equal factors.
(13 × 13)
Take one number from each group and multiply them to find the number whose square is 169.
13.
The square root of 169 is 13.
The final answer is 25 ÷ 169 = 5/13

Therefore, the square root of √(25 ÷ 169) = 5/13.

5. Find the value of √(196 ÷ 9)?

Solution:
Given the number is √(196 ÷ 9).
Firstly, separate the numerator and denominator.
√(196) ÷ √(9)
Find the separate Square Roots of the numerator and denominator.
Find the prime factors of √(196)
√(196) = 13 × 13
Grouping the factors into the pairs of equal factors.
(13 × 13)
Take one number from each group and multiply them to find the number whose square is 196.
13
The square root of 196 is 13.
Find the prime factors of √(9)
√(9) = 3 × 3
Grouping the factors into the pairs of equal factors.
(3 × 3)
Take one number from each group and multiply them to find the number whose square is 9.
3.
The square root of 9 is 3.
The final answer is 196 ÷ 9 = 13/3

Therefore, the square root of √(196 ÷ 9) = 13/3.

6. Find out the value of √25 × √16?

Solution:
Given that √25 × √16.
Find the separate Square Roots of the two numbers.
Find the prime factors of √(25)
√(25) = 5 × 5
Grouping the factors into the pairs of equal factors.
(5  × 5)
Take one number from each group and multiply them to find the number whose square is 25.
5
The square root of 25 is 5.
Find the prime factors of √(16)
√(16) = 4 × 4
Grouping the factors into the pairs of equal factors.
(4 × 4)
Take one number from each group and multiply them to find the number whose square is 16.
4.
The square root of 16 is 4.
The final answer is √25 × √16 = 5 × 4 = 20

Therefore, √25 × √16 = 20.

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