Page 46 - Math 7

Operations on Whole Numbers

1 = 1 = 1 × 1 o So, 1 is the square root of 1. o 1 = 1
2
4 = 2 = 2 × 2 o So, 2 is the square root of 4. o 4 = 2
2
9 = 3 = 3 × 3 o So, 3 is the square root of 9. o 9 = 3
2
16 = 4 = 4 × 4 o So, 4 is the square root of 16. o 16 = 4
2
Thus, a perfect square number is the product of two identical numbers and one of
the identical numbers is the square root of the square number.

The radical symbol ( ) is used to denote the square root of a number.
3.9 Process of finding square root

We usually use fractorisation method and division method to find the square root of
the given perfect square number.

Factorisation method to find square root

We usually use this method to find the square root of smaller perfect square numbers.
Let’s learn the process from the example given below.
Find the square root of 225 by factorisation method.

3 225 To find the square root, we should make the pairs of
3 75 two identical factors and the product of one of
the factors taken from each pair is the square
5 25 root of the number.

5
Now, 225 = 3 × 3 × 5 × 5
? 225 = 3 × 5 = 15

Division method to find square root
We use division method to find the square roots of the larger numbers. It is also
useful to find the square root of decimals. Let’s learn the process from the example
given below. (i) Starting from the unit place make the number pairs by using
bar mark just over each pair.
Find the square root of (ii) Take the first pair 68 and think of the largest perfect square
(i) 6889 (ii) 64516 which is equal to 68 or less than 68. It is 64.
(iii) Think of the square root of 64, it is 8.
8 68 89 83 (iv) Write 8 as the divisor and quotient. Multiply 8 u 8 = 64 and
+ 8 – 64 write just below 68, then subtract. The remainder is 4.
163 489 (v) Add 8 + 8 = 16 in the divisor side. It is the trial divisor.
+ 3 – 489 (vi) Bring down the other pair 89. Now, 489 is the new dividend.
166 0
(vii) 48 is 3 times divisible by 16. So, write 3 in the quotient and
6889 = 83 also in the divisor.
(viii) Find the product of 163 u 3 which is 489, and write it just
below 489 and subtract. The remainder is 0. Thus, 83 is the
square root of 6889.

Vedanta Excel in Mathematics - Book 7 44 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur