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.

3250

Answer 1

The square root of 3250 can be calculated by long division method as follows:

	57
5	${\displaystyle \overline{32} \overline{50}}$ -25
107	750  -749
	1

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 ${\displaystyle \sqrt{3249}}$ = 57