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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Before we proceed, we should know to predict the number of Remember
digits in the square root of a number. The square root of a two- If a perfect square has n digits,
digit number is a single-digit number and the square root of a then its square root contains:
three-digit or four-digit number is a two-digit number. n
• digits, if n is even.
Consider the number 56169. It has 5 digits, so the number of digits 2
n + 1
in its square root will be 5 + 1 = 3. • 2 digits, if n is odd.
2
Now, let us find the square root of the number 56169 as follows:

Steps Example
Step 1: Starting from the ones digit, make pairs of the digits 5 61 69
by placing a bar. The number of bars indicates the number of
digits in the square root.
2
Step 2: Think of the largest number whose square is equal to Since, 2 = 4 < 5, so we take the first divisor
or less than (nearest) the number under the extreme left bar. as 2,
Take this number as the divisor as well as quotient. Find the 2
product of the divisor and the quotient. Subtract this product 2 5 61 69
from the first or the leftmost pair. –4

Step 3: Next, bring down the next pair to the right of the 2
remainder. This becomes the next dividend.
2 5 61 69
–4

161

Step 4: Now, double the quotient obtained in step 2 and enter 2
it with a blank on the right for the next digit to find the next 2 5 61 69
possible divisor.
–4
4_ 161

Step 5: To fill in the blank, guess a possible digit such that the 2 3
product of the new divisor and this digit is equal to or just less 2 5 61 69
than the new dividend.
–4
Since 43 × 3 = 129 < 161 and 44 × 4 = 176 > 161, so the new divisor 43 161
is 43.
–129
After getting the new divisor, subtract the product of divisor
and the digit selected from the new dividend. 32
Step 6: Repeat the steps 2-5 till all the pairs have been taken 2 3 7
up. The quotient so obtained is the required square root of the 2 5 61 69
given number. –4
43 161
–129
467 3269
–3269
0
\ 56169 = 237

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