Question

Find the square root of 100 by the method of repeated subtraction.
A) 10
B) 11
C) 9
D) 12

Answer 1

Hint: If you need to find the square root of a number \[n\], subtract odd numbers from it like 1 from \[n\], 3 from the \[n-1\] and so on, till 0 is obtained.

Complete step-by-step answer:
You need to find the square root of 100.
Now, the method of repeated subtraction includes subtracting consecutive odd numbers from the number whose square root is to be determined until 0 is obtained. The number of steps until 0 is reached gives the square root of the number.
So, it follows,
\[100 – 1 = 99\]
\[99 – 3 = 96\]
\[96 – 5 = 91\]
\[91 – 7 = 84\]
\[84 – 9 = 75\]
\[75 – 11 = 64\]
\[64 – 13 = 51\]
\[51 – 15 = 36\]
\[36 – 17 = 19\]
\[19 – 19 = 0\]
Since 0 occurs in the 10th step, so the square root of 100 is 10.

Hence, the correct option is (A).

Note: The square root of a number can also be determined using the unique factorisation method, where the number can be expressed as a product of prime factors. And, then determine the product of repeated factors.