Question

What is the rule to find the number of non-square numbers between two consecutive perfect squares?

Answer 1

In general, we can say that there are 2n non-perfect square numbers between the squares of the numbers n and (n + 1).

For example, consider,

$n=4andn+1=5$

$4^2=16and{5}^2=25$

The non-square numbers between 16 and 25 are 17, 18, 19, 20, 21, 22, 23, 24. i.e., 8 numbers

Now, $8=2\times 4$

$\Rightarrow$ There are 2n non-perfect square numbers between the squares of the numbers n and (n + 1).