Question

How many numbers lie between squares of the following numbers ?
(i) $12$ and $13$
(ii)$25$ and $26$
(iii) $99$ and $100$

Answer 1

(i) ${12}^2=144$
${13}^2=169$
$169-144=25$
So, there are $25-1=24$ numbers lying between ${12}^2$ and ${13}^2$

(ii) ${25}^2=625$
${26}^2=676$
$676-625=51$
So, there are $51-1=50$ numbers lying between ${25}^2$ and ${26}^2$

(iii) ${99}^2=9801$
${100}^2=10000$
$10000-9801=199$
So, there are $199-1=198$ numbers lying between ${99}^2$ and ${100}^2$