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

Practice Time 5D

1. Use division method to find the square root of the following.

(a) 9604 (b) 7225 (c) 42849 (d) 95481
2. Find the least number which must be subtracted from each of the following numbers so as to get
a perfect square. Also, find the square root of the perfect square so obtained.
(a) 1750 (b) 1825 (c) 6412 (d) 390700
3. Find the smallest number which must be added to each of the following numbers to get a perfect
square. Also find the square root of the perfect square so obtained.
(a) 402 (b) 1989 (c) 3250 (d) 9699

4. Find the least and greatest 6-digit number that is a perfect square.
5. Find the greatest number with five digits which is a perfect square. Also, find the square root of the
number so obtained.
Square Root of Decimal Numbers

We know that a decimal number has two parts—the decimal part and the integral part.
For example, in 16.25, we have

16 . 25
Integral part Decimal part
For finding square root of decimal numbers, we count from left to right for the decimal part and
from right to left for the integral part. If decimal part has odd number of digits, put zero(s) in
extreme right to make them pairs. The square root of a decimal
For example, 2.009601 → 2 . 00 96 01; 392.56 → 3 92 . 56; Note: number will also contain as many
772.355 → 7 72 . 35 50 decimal places as there are bars.

To find the square root of above decimal number, we consider the number 477.4225 and proceed
as follows:
Steps Example

Step 1: Place bars on the integral part of the number from right to left starting Right to left
from the decimal point. 4 77.4225

Step 2: Place bars on the decimal part on every pair of digits beginning with Right to left Left to right
the first decimal place. 4 77.42 25
Step 3: Start finding the square root by the division process in a similar manner. 21.85

Place decimal point in the quotient as soon as the integral part is exhausted. 2 4 77.42 25
–4
Stop when the remainder becomes zero (0).
41 077
–41
428 3642
–3424
4365 21825

–21825
0
Step 4: The quotient is the square root of the given number. \ 477 4225 = 21 85
.
.
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