Question

How many numbers lie between squares of the following numbers?

1. $12$ and $13$
2. $25$ and $26$
3. $99$ and $100$

Answer 1

We know that there will be $2n$ numbers in between the squares of the numbers $n$ and $(n + 1)$.
(i) Between $12^2$ and $13^2$, there will be $2 \times 12 = 24$ numbers

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(ii) Between $25^2$ and $26^2$, there will be $2 \times 25$ = $50$ numbers

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(iii) Between $99^2$ and $100^2$, there will be $2 \times 99$ = $198$ numbers