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Q)

Find the least number which should be added to 3579 to get a perfect square

Find the least number which should be added to 3579 to get a perfect square.

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A)
21. That makes it 3579+21=3600. 3600=60*60. If there is a number between 3579 and 3600 which is a square, then the difference of the two squares will be less than 21. $60^2 - a^2 < 21$. If you expand, you see that the product of two integers 60-a and 60+a is always bigger than 21.
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