What is the least number that must be taken away from 7581 so that the result is a perfect square?

Look for the largest square below 7581. Since $87^2=7569$ and $88^2=7744$, we subtract 7581 − 7569 = 12 to land on $87^2$. The trap is 163: that is 7744 − 7581, the amount you would ADD to reach the next square upwards, which answers a different question. 87 is merely the square root.