Question

 Find the least number that must be subtracted from 7581 to obtain a perfect  square.

Answer 1

the least number that can be subtracted is 7581 - 87² = 12 

Answer 2

We solve the √7581 it does not completely rooted.We are left with Quotient=87 and Remainder=12.
If we subtract 7581-12 the answer is 7569,also √7569=87 or 7569=(87)².
So the least number required is 12.