find the smallest number which must be subtracted from 4931 to make them a perfect square .
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You know that 49 is a perfect square as 7*7 = 49.
Hence 70*70 = 4900 is also a perfect square. Try the next number 71*71 = 5041 which is also a perfect square. Now you can be sure that the given number (4931) is not a perfect square.
Now check how much does the given number deviate from these two closest perfect squares. If it deviates lesser from the larger one, subtract a negative number otherwise a positive number, to get to your answer.
(5041–4931 = 110) > (4931–4900 = 31).
Therefore 31 is your answer!
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