# Find the least number which must be subtracted from each of the following numbers so as to get a perfect square.

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Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

(i) 402 (ii) 1989

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(i) The square root of 402 can be calculated by long division method as follows. The remainder is 2. It represents that the square of 20 is less than 402 by 2.

Therefore, a perfect square will be obtained by subtracting 2 from the given number 402.

Therefore, required perfect square = 402 − 2 = 400 And, √400 = 20

(ii) The square root of 1989 can be calculated by long division method as follows.  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, √1936 = 44

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