# Square Root of Rational Numbers

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Square root of rational numbers in the form of fractions

Step I: Obtain the fraction
Step II: If the given square root of the numerator and the denominator are the square roots of numerator and denominator respectively of the given fraction.
Step III: Find the square root of the numerator and denominator separately.
Step IV: Obtain the fraction whose numerator and denominator are the square roots of numerator and denominator respectively of the given fraction.
Step V: The fraction obtained in Step IV is the square root of the given fraction.

Examples on square root of rational numbers

1) Find the square root of rational numbers 256/441.

Solution :
We have, √(256/441) = √(256)/√(441)

First find the square roots of 256 and 441 separately using prime factorization method.
256 = 2 x 128
= 2 x 2 x 64
= 2 x 2 x 2 x 32
= 2 x 2 x 2 x 2 x 16
= 2 x 2 x 2 x 2 x 2 x 8
= 2 x 2 x 2 x 2 x 2 x 2 x 4
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
∴ √256 = √(2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)
∴ √256 = 16
Now, find the square root of 441,
441 = 3 x 147
= 3 x 3 x 49
= 3 x 3 x 7 x 7
∴ √441 = √(3 x 3 x 7 x 7)
∴ √441 = 21

⇒√(256/441) = 16/21
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2) Find the square root of 0.0196.

Solution:
First write 0.0196 in fraction form.
0.0196 = 196/10000
√(196/10000) = √(196)/√ (10000) = 14/100
∴0.0196 = 14/100 = 0.14
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3) The area of a square field is 30(1/4)sq.m. Calculate the length of the side of the square.

Solution :
First convert 30(1/4) mixed fraction to improper fraction.
30(1/4) = 121/4
Now find the square root of the area of square field, as (Area = side x side)
Side = √(area)
Side = √(121/4)
side = √121/√4
Side = 11/2
∴ Each side of square field = 5.5 m
Squares and Square roots

Introduction of Squares and Square Roots
Perfect Squares or not
Properties of Square Numbers
Short cut method to find squares
Introduction of Square Roots
Properties of Square Roots
Square root by Prime factorization method
Square root by long division method
Square root of rational numbers
Square root of Decimals
Square root by estimation method

From squares and square roots to Exponents