Page 69 - Start Up Mathematics_8 (Non CCE)

1,369 1,369 37
0.001369 = = = = 0.037
10,00,000 1,000 1,000 1,000
¥
0.002025 + 0.001369 0.045 0.037+ 0.082 82 41
\ = = = =
-
0.002025 - 0.001369 0.045 0.037 0.008 8 4
EXERCISE 3.7

1. Find the square root of the following:
(a) 62.41 (b) 1.8225 (c) 0.0441 (d) 184.96 (e) 0.00073441
(f) 0.002704 (g) 2.2201 (h) 74.4769 (i) 235.3156 (j) 54.0225
2
2. The area of a square plot is 30.1401 m . Find its side.
3. Find the square root of 7,60,384. Use this to find the value of 76.0384 - 0.760384 .
75.69 + 31.36
4. Find the square root of 3,136 and 7,569. Using these values, find the value of .
75.69 - 31.36

5. Find the square root of 625 and 441. Using these values, find the value of 6.25 ¥ 0.0441.

Approximating the Value of Square Roots by Long Division Method
Step 1: Determ ine the number of decimal places upto which the square root of a number is to be calculated,
say, n places of decimal.
Step 2: Count the digits in the decimal part of the number. If the number of digits is less than 2n, then add
suitable number of zeros to the far right side of the decimal part so as to make the digits 2n.
Step 3: Use the long division method of finding the square root upto (n + 1) places of decimal.
Step 4: If the digit at (n + 1)th decimal place is less than 5, then delete it to get the answer correct to n decimal
places. If however, the digit at (n + 1)th decimal place is > 5, then increase the digit at the nth place by
1 and delete the digit at the (n + 1)th place. This is called rounding off.
3
Example 25: Find the square root of (a) 436.235 and (b) 12 upto three places of decimal.
4
3 51
Solution: (a) (b) 12 =
4 4
20.8862 = 12.75 3.5707

2 4 36. 23 50 00 00 12 3 = 12.75 3 12. 75 00 00 00
4 4 9
40 36 65 375
00 325
408 3623 707 5000
3264 4949
4168 35950 7140 5100
33344 0000
41766 260600 71407 510000
250596 499849
417722 1000400 10151
835444

164956

61