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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.
825
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Solution
The square root of 825 can be calculated by the long division method as follows:
| 28 | |
| 2 | `bar8 bar25` -4 |
| 48 | 425 -384 |
| 41 |
The remainder is 41. It represents that the square of 28 is less than 825 by 41. Therefore, a perfect square can be calculated by subtracting 41 from the given number 825.
Therefore, required perfect square = 825 − 41 = 784
And `sqrt(784)` = 28
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