Page 17 - NCERT Books

SQUARES AND SQUARE ROOTS 105

TRY THESE

Without calculating square roots, find the number of digits in the square root of the
following numbers.
(i) 25600 (ii) 100000000 (iii) 36864

Example 9: Find the square root of : (i) 729 (ii) 1296
Solution:
36
(i) 27 (ii)
3 1296
2 729
– 4 – 9
47 329 Therefore 729 = 27 66 396 Therefore 1296 = 36
396
329 0
0

Example 10: Find the least number that must be subtracted from 5607 so as to get 74
a perfect square. Also find the square root of the perfect square.
7 5607
Solution: Let us try to find 5607 by long division method. We get the – 49
2
remainder 131. It shows that 74 is less than 5607 by 131. 144 707
This means if we subtract the remainder from the number, we get a perfect square. –576
Therefore, the required perfect square is 5607 – 131 = 5476. And, 5476 = 74. 131

Example 11: Find the greatest 4-digit number which is a perfect square. 99
Solution: Greatest number of 4-digits = 9999. We find 9999 by long division 9 9999
method. The remainder is 198. This shows 99 is less than 9999 by 198. – 81
2
This means if we subtract the remainder from the number, we get a perfect square. 189 1899
Therefore, the required perfect square is 9999 – 198 = 9801. – 1701
198
And, 9801 = 99

Example 12: Find the least number that must be added to 1300 so as to get a 36
perfect square. Also find the square root of the perfect square. 3 1300
– 9
Solution: We find 1300 by long division method. The remainder is 4.
66 400
2
This shows that 36 < 1300.
– 396
Next perfect square number is 37 = 1369.
2
2
Hence, the number to be added is 37 – 1300 = 1369 – 1300 = 69. 4
6.6 Square Roots of Decimals

Consider 17.64

Step 1 To find the square root of a decimal number we put bars on the integral part
(i.e., 17) of the number in the usual manner. And place bars on the decimal part