Question

There are non-square natural numbers between the squares of 4 and 5.

• A. three
• B. six
• C. eight
• D. ten

Answer 1

The correct option is C eight

We know that between $n^2$ and $(n+1{)}^2$, there are 2n non-square natural numbers.
Example: Between $2^2$ and $3^2$ there are $2\times 2=4$ non-square natural numbers.
These numbers are 5, 6, 7 and 8.

$\Rightarrow$ Between $4^2$ and $5^2$, there are $2\times 4=8$ non-square numbers.