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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.
1825
Solution
The square root of 1825 can be calculated by long division method as follows.
| 42 | |
| 4 | `bar18 bar25` -16 |
| 82 | 225 -164 |
| 61 |
The remainder is 61.
Clearly, 422 = 1764 < 1825
432 = 1849 > 1825
The number that should be added is 1849 - 1825 = 24, and the square root of 1849 is 43.
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