Question

The number of non-perfect square numbers between the squares of two consecutive integers n and (n + 1) is __________.

• A. 2(n + 1)
• B. 2n - 1
• C. 2n
• D. 2n + 1

Answer 1

The correct option is C 2n

The squares of n and (n + 1) are $n^2$ and ${(n+1)}^2$.

So, the number of non-perfect square numbers between these two squares is
${(n+1)}^2-n^2-1$
( e.g. the number of natural numbers between 4 and 7 is 7 - 4 - 1 = 2)
=$n^2+2n+1-n^2-1$
= 2n
So, the correct option is B.