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There are 2n Non Perfect Square Numbers Between the Squares of the Numbers n and (n+1)

There are 16 ...

Question

There are 16 non-perfect square numbers between the square of the numbers $n$ and $(n + 1)$ . Find $(n + 1)^{2}$ .

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Solution

The correct option is C 81
Since there are '2n' non perfect square numbers between the squares of the numbers 'n' and '(n+1)'

Given: Number of non-perfect square numbers = 16
$\Rightarrow 2 n = 16 \Rightarrow n = 8$
$∴ n = 8, (n + 1) = 9$
$\Rightarrow The numbers are 8 and 9$
$\Rightarrow (n + 1)^{2} = 9^{2} = 81$

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