# 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**

**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

• 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

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