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Question
Find the least number which must be subtracted from the following number so as to get a perfect square. Also find the square root of the perfect square so obtained.
1989
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Solution
The square root of 1989 can be calculated by long division method as follows.
| 44 | |
| 4 | `bar19 bar89` -16 |
| 84 | 389 389 |
| 53 |
The remainder is 53. It represents that the square of 44 is less than 1989 by 53. Therefore, a perfect square will be obtained by subtracting 53 from the given number 1989.
Therefore, required perfect square = 1989 − 53 = 1936
And `sqrt(1936)` = 44
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