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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.
4000
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Solution
The square root of 4000 can be calculated by the long division method as follows:
| 63 | |
| 6 | `bar40 bar00` -36 |
| 123 | 400 -369 |
| 31 |
The remainder is 31. It represents that the square of 63 is less than 4000 by 31. Therefore, a perfect square can be obtained by subtracting 31 from the given number 4000.
Therefore, required perfect square = 4000 − 31 = 3969
∴ `sqrt(3969)` = 63
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