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Question
Find the least number which must be added to the following number so as to get a perfect square. Also find the square root of the perfect square so obtained.
252
Solution
The square root of 252 can be calculated by long division method as follows.
| 15 | |
| 1 | `bar2 bar52` -1 |
| 25 | 152 -125 |
| 27 |
The remainder is 27.
Clearly, 152 = 225 < 252
162 = 256 > 252
∴ The number to be added is 256 − 252 = 4
and the square root of 256 is 16.
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