Page 29 - SM inner class 8.cdr

3. Finding Square Root By Repeated Solution: Let us try to find the square root of
Subtraction 26535 by long division method:
162
Let us recall odd numbers 1, 3, 5, 7, 9 .....
1 2 65 35
Take the given number whose square root is to +1 1
be found out and follow these steps: 26 165
Step 1. Take the given number and +6 – 156
subtract the odd numbers 1, 3, 5, 7 243 935
..... successively from it. 3 644
Step 2. We will get zero at some stage 294
during subtraction if the number is
a perfect square. 291 is the least number to be subtracted from
26535 to make it a perfect square
Step 3. Stop at the point where zero is So, the least number to be subtracted from
obtained after subtraction. Declare 26535 is 291.
the number of times, the Required perfect square number = (26535 -
subtractions is performed, as the 291) = 26244
square root of given number.
And, 26244 = 162.
Example 14. Find the square root of 81.
Example 17. What least number must be
(1) 81 1 80- = (2) 80 - 3 = 77 added to 7344 to make it a perfect square?
(3) 77 - 5 = 72 (4) 72 - 7 = 65 Solution: We go through the long division

(5) 65 - 9 = 56 (6) 56 11 45- = steps to find the square root of 7344. In the
(7) 45 13- = 32 (8) 32 15 17- = second division step.
(9) 17 17- = 0 8
8 73 44
We have subtracted successive odd numbers
+8 64
from 81. We performed subtraction 9 times to
16 944
obtain 0. Therefore, 81 = 9
(
Note: The method of suc ces sive sub trac tion to find We find that 165 ´ 5 = 825 < 944)
square root is use ful for small per fect square while 166 ´ 6 = 996 > 944)
(
num bers. 2 2
Hence 7344 lies between 85 and 86 .
To make it perfect square the least number
Word Problems
2
that should be added is 86 - 73
Example 15. Find the cost of putting fence 44 = 7396 - 7344 = 52
around a square field whose area is 9 hectares Example 18. Find the greatest number of four
if fencing costs ` 4 per metre.
digit which is a perfect square.
Solution: Area of the square field = (9 ´ 10000)
2
2
2
m = 90000 m [1 hectare = 10000 m ] Solution: Greatest number of 99
four digits = 9999.
Length of each side of the field = 90000 m = Let us try to find the square 9 99 99
300 m. +9 81
root of 9999.
Perimeter of the field = (4 ´ 300) m = 1200 m. 189 1899
2
)
This shows that (99 is less +9 1701
Cost of fencing = ` (1200 ´ 4) = ` 4800.
than 9999 by 198. 198
Example 16. What least number must be So, the least number to be
subtracted from 26535 to get a perfect square? subtracted is 198.
Also, find the square root of this perfect Hence, the required number is (9999 - 198) =
square. 9801.

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Mathematics In Focus - 8