Question

What is the least number that must be subtracted from $5,607$ to get a perfect square ?

• A. $125$
• B. $129$
• C. $131$
• D. $135$

Answer 1

The correct option is C $131$

Let's try to find $\sqrt{5607}$ by long division method.

• We get the remainder as $131.$
• This shows that ${74}^2<5607$ by $131.$
• This means if we subtract the remainder $\left(131\right)$ from the dividend $(5,607),$ we get a perfect square.

Therefore, the least number to be subtracted from $5,607$ to get a perfect square is $\underset{–}{131}.$

And, the perfect square number would be $(5,607-131)=5,476={74}^2.$

$\therefore$ Option (c.) is the correct choice.