Square Root of Rational Numbers

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

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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

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