What least number should be subtracted from 5634 so that the result becomes a perfect square?

Principle: the least number to subtract is the difference between the given number and the greatest perfect square below it. 1. Check nearby squares: $75^2=5625$ and $76^2=5776$. 2. Since $5625<5634<5776$, the nearest lower perfect square is 5625. 3. Therefore the least number to subtract is $5634-5625=9$. Why others fail: subtracting 4 gives 5630, subtracting 8 gives 5626, and subtracting 10 gives 5624 none of these is a perfect square.