Question

How many numbers lie between squares of the following numbers?

$\left(i\right)12$ and $13$

$\left(ii\right)25$and $26$

$\left(iii\right)99$ and $100$

Answer 1

We know that there will be $2n$ numbers in between the squares of the numbers $n$ and $n+1$.

$\left(i\right)12$ and $13$

Between ${12}^2$ and ${13}^2$ there will be $2\times 12=24$ numbers.

${12}^2=144,{13}^2=169$

So the numbers between $144$ and $169$ are

$145,146,147,.......168$ are $24$ numbers.

Similarly, we can evaluate the remaining two questions.

$\left(ii\right)25$and $26$

Between ${25}^2$ and ${26}^2$ there will be $2\times 25=50$ numbers

$\left(iii\right)99$ and $100$

Between ${99}^2$ and ${100}^2$ there will be $2\times 99=198$ numbers.