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.

4000

Answer 1

The square root of 4000 can be calculated by the long division method as follows:

	63
6	`bar40  bar00` -36
123	400    -369
	31

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

∴ `sqrt(3969)` = 63