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

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)

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)

⇒√(256/441) = 16/21

_________________________________________________________________

2) Find the square root of 0.0196.

First write 0.0196 in fraction form.

0.0196 = 196/10000

√(196/10000) = √(196)/√ (10000) = 14/100

________________________________________________________________

3) The area of a square field is 30(1/4)sq.m. Calculate the length of the side of the square.

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

• 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

Home Page

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers