Question

find the least number that is to be subtracted from 4000 to make it perfect square

Answer 1

The square root of 4000 is 63 and change

The square of 63 is 3969

4000–3969=31

So 31 is the least you can subtract from 4000 to reach a perfect square

You could also subtract negative 96, to reach 4096, the square of 64, however, for this to be the “least” you would have to be using the definition of least which consists of “furthest left on the number line” but there are infinite numbers, each further left than the next, which can be subtracted from 4000 to give progressively larger perfect squares.

Using the definition of least “closest to zero” 31 is less than -96.

So it’s 31, or there is no such number, only an infinity of negatives.