Question

If M is a square number, what is the next immediate square number?

• A. $M+5$
• B. $M+2\sqrt{M}+1$
• C. $M^2+2M$
• D. $M+2\sqrt{M}-1$

Answer 1

The correct option is B $M+2\sqrt{M}+1$

We can solve this question using option elimination.
Consider M = 25
Then $M+5=25+5=30$ (Which is not a perfect square)
So option 1 is eliminated.
$M+2\sqrt{M}+1=25+2\sqrt{25}+1=25+10+1=36$ (Which is a perfect square)
So option 2 is correct.
$M^2+2M=(25{)}^2+2(25)=625+50=675$ (Which is not a perfect square)
So option 3 is eliminated.
$M+2\sqrt{M}-1=\left(25\right)+2\sqrt{25}-1=25+10-1=34$ (Which is not a perfect square)
So option 4 is eliminated.
Hence only option 2 is correct.