Question

There are non-square numbers between $n^2$ and $(n+2{)}^2$.

• A. $2n+4$
• B. $2n$
• C. $4n+2$
• D. $2n+2$

Answer 1

The correct option is C $4n+2$

There is one square number between $n^2$ and $(n+2{)}^2$ which is $(n+1{)}^2$.

There are $2n$ non-square numbers between $n^2$ and $(n+1{)}^2$, and $2(n+1)$ non square numbers between $(n+1{)}^2$ and $(n+2{)}^2$.

Hence, in total, there are $2n+2(n+1)=4n+2$ non square numbers in between $n^2$ and $(n+2{)}^2.$