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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.
6412
Solution
The square root of 6412 can be calculated by the long division method as follows:
| 80 | |
| 8 | `bar64 bar12` -64 |
| 160 | 012 00 |
| 12 |
The remainder is 12.
Clearly, 802 = 6400 < 6412
812 = 6561 > 6412
The number that should be added is 6561 − 6412 = 149, and the square root of 6561 is 81.
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