Question

How to find square root?

Answer 1

Square Roots can be found by following methods
1. Repeated Subtraction Method
2. Prime Factorization Method
3. Long Division Method.
The following steps to find the square root of a given number using Repeated subtraction method
1. Subtract successive odd numbers from the given number starting from 1 till the difference becomes zero.
2. Count the number of steps it took to get the difference as zero.
Consider $\sqrt{81}$. Then,
(i) 81 - 1 = 80 (ii) 80 - 3 = 77 (iii) 77 - 5 = 72 (iv) 72 - 7 = 65 (v) 65 - 9 = 56 (vi) 56 - 11 = 45 (vii) 45 - 13 = 32 (viii) 32 - 15 = 17 (ix) 17 - 17 = 10

The following steps to find the square root by prime factorization method
1. Find the prime factors of the given number.
2. Form pairs of prime factors.
3. Take one prime factor from each pair of prime factors of the given number.
4. Find the product of these prime factors to get the square root of the given number.If prime factors of a number do not occur in pairs, the given number is not a perfect square.

$324=\underset{–}{2\times 2}\times \underset{–}{3\times 3}\times \underset{–}{3\times 3}=2^2\times 3^2\times 3^2=(2\times 3\times 3{)}^2$
$So,\sqrt{324}=2\times 3\times 3=18$
The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero.