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

1.1k views

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) 3250 (ii) 825 (iii0 4000

by (24.8k points)
selected

(i) The square root of 3250 can be calculated by long division method as follows. The remainder is 1. It represents that the square of 57 is less than 3250 by 1.

Therefore, a perfect square can be obtained by subtracting 1 from the given number 3250.

Therefore, required perfect square = 3250 − 1 = 3249

And,  3249 = 57

(ii) The square root of 825 can be calculated by long division method as follows.  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,  784 = 28

(iii) The square root of 4000 can be calculated by long division method as follows. 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

And,  3969 = 63