# SQUARE ROOTS OF FRACTIONS AND DECIMALS

## About "Square roots of fractions and decimals"

Square roots of fractions and decimals :

Finding square roots is the opposite process squaring.

1²  =  1, the square root of 1 is 1.

2²  =  4, the square root of 4 is 2.

3²  =  9, the square root of 9 is 3.

4²  =  16, the square root of 16 is 4.

## How to find a square root of a fraction ?

• To find the square root of a fraction, we have to take separate square roots for both numerator and denominator.
• After taking square roots of both numerator and denominator separately, we can combine them.

## How to find a square root of a decimal ?

• To find the square root of a decimal number, first we have to remove the decimal by multiplying the numerator and denominator by the multiples of 10.
• According to the given number, we have to decide whether the number to be multiplied by 10, 100 or 1000 etc in order to remove the decimal point.
• After removing the decimal point, we will get a fraction and now we have to take separate square roots.

Let us see some examples based on the above concepts.

Example 1 :

Find the square root of the following decimal number

2.56

Solution :

Since we have two numbers after the decimal point, we have to multiply both numerator and denominator by 100.

2.56  =  2.56 x (100/100)

=  √(256/100)

 Now take separate square roots for both numerator and denominator.  =  √(256/100)  =  √256/√100√256 = √(2x2x2x2x2x2x2x2)√100  = √(2x2x5x5)

256 = 2 x 2 x 2 x 2 = 16

100  =  2 x 5  = 10

√256/√100  =  16/10  = 1.6

2.56  =  1.6

Example 2 :

Find the square root of the following decimal number

51.84

Solution :

Since we have two numbers after the decimal point, we have to multiply both numerator and denominator by 100.

Here 51.84 can be considered as 51.84/1

√(51.84/1)  =  (51.84/1) x (100/100)

=  √(5184/100)

 Now take separate square roots for both numerator and denominator.  =  √(5184/100)  =  √5184/√100√5184= √(2x2x2x2x2x2x3x3x3x3)√100  = √(2x2x5x5)

√1584 =  = 2 x 2 x 2 x 3 x 3 = 72

100  =  2 x 5  = 10

√1584/√100  =  72/10  = 7.2

√15.84  =  7.2

Example 3 :

Find the square root of the following decimal number

0.2916

Solution :

Since we have four digits after the decimal point, we have to multiply both numerator and denominator by 10000.

Here 0.2916 can be considered as 0.2916/1

√(0.2916/1)  =  (0.2916/1) x (10000/10000)

=  √(2916/10000)

 Now take separate square roots for both numerator and denominator.  =  √(2916/10000)  =  √2916/√10000√2916= √(2x2x3x3x3x3x3x3)√10000  = √(5x5x5x5x2x2x2x2)

√2916 =  = 2 x 3 x 3 x 3 = 54

10000  =  5 x 5 x 2 x 2  = 100

√2916/√10000  =  54/100  = 0.54

√0.2916  =  0.54

After having gone through the stuff given above, we hope that the students would have understood "Square roots of fractions and decimals".

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