What least number should be subtracted from 5634 so that the result becomes a perfect square?
A4
B8
C9
D10
Answer & Solution
Correct answer: C. 9
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.
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