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SQUARES AND SQUARE ROOTS 107

Solution: Let the number of rows be x 49
So, the number of columns = x 4 2401
Therefore, number of students = x × x = x 2 –16
2
Thus, x = 2401 gives x = 2401 = 49 89 801
The number of rows = 49. 801
0
6.7 Estimating Square Root

Consider the following situations:
1. Deveshi has a square piece of cloth of area 125 cm . She wants to know whether
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she can make a handkerchief of side 15 cm. If that is not possible she wants to
know what is the maximum length of the side of a handkerchief that can be made
from this piece.
2. Meena and Shobha played a game. One told a number and other gave its square
root. Meena started first. She said 25 and Shobha answered quickly as 5. Then
Shobha said 81 and Meena answered 9. It went on, till at one point Meena gave the
number 250. And Shobha could not answer. Then Meena asked Shobha if she
could atleast tell a number whose square is closer to 250.
In all such cases we need to estimate the square root.

We know that 100 < 250 < 400 and 100 = 10 and 400 = 20.
So 10 < 250 < 20
But still we are not very close to the square number.
2
2
We know that 15 = 225 and 16 = 256
Therefore, 15 < 250 < 16 and 256 is much closer to 250 than 225.
So, 250 is approximately 16.

TRY THESE

Estimate the value of the following to the nearest whole number.
(i) 80 (ii) 1000 (iii) 350 (iv) 500

EXERCISE 6.4

1. Find the square root of each of the following numbers by Division method.
(i) 2304 (ii) 4489 (iii) 3481 (iv) 529
(v) 3249 (vi) 1369 (vii) 5776 (viii) 7921
(ix) 576 (x) 1024 (xi) 3136 (xii) 900
2. Find the number of digits in the square root of each of the following numbers (without
any calculation).
(i) 64 (ii) 144 (iii) 4489 (iv) 27225
(v) 390625