Example 8:
Find the square root of 8281
Solution:
Example 9:
Find the greatest four digit
number which is a perfect square
Solution:
Greatest four digit number is 9999
We find square root of 9999 by division method.
The remainder 198 shows that it is less than 9999 by 198
This means if we subtract 198 from 9999, we get a perfect square.
∴ 9999 – 198 = 9801 is the required perfect square.
Example 10: Find the least number which must be subtracted from 4215
to make it a perfect square?
Solution:
We find by division method that
The remainder is 119
This means, if we subtract 119 from 4215. We get a perfect square.
Hence, the required least number is 119.
6.8 Square roots of decimals using division method :
Let us begin with the example 17.64
Step 1: Place the bars on the integral part of the number i.e. 17 in the
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usual manner. Place the bars on every pair of decimal part from
left to right
Step 2: Find the largest number (i.e. 4) whose square is less than or
equal to the first pair of integral part (i.e. 17). Take this number
4 as a divisor and the first pair 17 as the dividend. Get the
remainder as 1.
Divide and get the remainder i.e. 1
Step 3: Write the next pair (i.e. 64) to the right of the remainder to get
164, which becomes the new dividend.