Question

Find the square root of the number 144 using repeated subtraction method.

Answer 1

Hint:-Before solving this question we must know about the Repetitive Subtraction Method that is used to find Square Roots of different numbers.

Complete step-by-step answer:
REPETITIVE SUBTRACTION: To find Square root using the Repeated Subtraction method, we subtract consecutive odd numbers from the number of which the square root is to be calculated till we obtain 0. The Square root will be equal to the total numbers subtracted.
Let us take an example. Say 81. So, to find whether 81 is a perfect square or not and the square root of 81, we need to subtract consecutive odd numbers from 81.
81 – 1 = 80
80 – 3 = 77
77 – 5 = 72
72 – 7 = 65
65 – 9 = 56
56 – 11 = 45
45 – 13 = 32
32 – 15 = 17
17 – 17 = 0
So, we can say that 81 is a perfect square and the square root of 81 is 9 as the total number of numbers subtracted from 81 are 9.

Let us now find the square root of 144.
144 – 1 = 143
143 – 3 = 140
140 – 5 = 135
135 – 7 = 128
128 – 9 = 119
119 – 11 = 108
108 – 13 = 95
95 – 15 = 80
80 – 17 = 63
63 – 19 = 44
44 – 21 = 23
23 – 23 = 0
So, the number 144 is a perfect square and the square root of 144 is 12 as the total number of numbers subtracted from 144 are 12.
Therefore, the square root of 144 is 12.

Note:-One should subtract only the odd numbers from the number of which the square root is to be calculated.
If even numbers are subtracted from the number of which the square root is to be calculated, then the answer would come out to be wrong.