Question

Find the square root of 100 by the method of repeated subtraction.

Answer 1

Hint: To find the square root of a number by subtraction method, we will subtract successive odd numbers from the number till we obtain 0. Total number we subtract is the square root of the number. So here we will subtract one by one from successive odd numbers like 1, 3, 5, 7,… until we obtain 0.

Complete step by step solution:Here the given number is 100. We need to find the square root of the number 100 by the method of subtraction.
To find the square root of a number by subtraction method, we will subtract successive odd numbers from the number till we obtain 0. Total number we subtract is the square root of the number.
So here we will subtract one by one from successive odd numbers like 1, 3, 5, 7,… until we obtain 0.
Let’s start subtracting one by one odd number form 100.
So, $100 - 1 = 99$
Subtracting next odd number, $99 - 3 = 96$
Subtracting next odd number, $96 - 5 = 91$
Subtracting next odd number, $91 - 7 = 84$
Subtracting next odd number, $84 - 9 = 75$
Subtracting next odd number, $75 - 11 = 64$
Subtracting next odd number, $64 - 13 = 51$
Subtracting next odd number, $51 - 15 = 36$
Subtracting next odd number, $36 - 17 = 19$
Subtracting next odd number, $19 - 19 = 0$
Since, we have subtracted 10 odd numbers then we obtained 0. So, the square root of 100 is 10.

Note: There is an alternate method to find the square root of a number by prime factorization method.
In the prime factorization method we represent the number as an even power of prime factors. So firstly represent the number in power form of prime factors. As a number $100 = 4 \times 25 = 2 \times 2 \times 5 \times 5$. Representing in power form as $100 = {2^2} \times {5^2}$. Taking square root on both sides as, $\sqrt {100} = \sqrt {{2^2} \times {5^2}} $. So, $\sqrt {100} = 2 \times 5 = 10$. So, the square root of number 100 is 10.