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

As 360 is closer to 361 than to 324, so 360 is approximately equal to 19.

Sometimes we have to find the square root of non-perfect squares up to certain decimal places.
Let us find the square root of 5 up to two decimal places.

We write 5 as 5.000000 (writing as many zeros as required to make three pairs of numbers in the
decimal part).
2.236
2 5.00 00 00

–4 Remember
42 100 If we are asked to find the square root up
to two decimal places, we should find the
–84 square root up to 3 places and then round
443 1600 off. Similarly, if it is asked to find the square
–1329 root up to three places, we should find it up
to 4 places and then round off.
4466 27100
–26796
304

Since, the digit at the third place is greater than 5, so we round up 2.236 to 2.24.
\ 5 = 2.236 ≈ 2.24
2
Example 31: Find the square root of 4 up to two decimal places.
3
Solution: We have

2 14 14 3 42 42
4 = = × = =
3 3 3 3 9 3

6.4807
6 42.00 00 00 00
–36
124 600 Quick Check

–496 Find the square root of the
1288 10400 following up to two decimal
–10304 places.
12960 9600 1. 30 2. 4 1

– 0 2
129607 960000
– 907249
52751

42 6 4807
.
Thus, = = 2.1602
3 3
2
So, 4 = 2.16 (up to two decimal places).
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