How many integer lie between the square of the following number $15$ and $16$.

Given: Two numbers $15$ and $16$.

To do: To find the number of integers lying between the square of the following number $15$ and $16$.

The square of $15=15^2=15\times15=225$

The square of $16=16^2=16\times16=256$

The numbers lying between the square of $15$ and $16$ are between $225$ and $256$.

$i.e.,\ 226,\ 227,\ 228,\ ......, 255$.

It is an A.P., Here $a=226,\ d=1,\ l=255,\ n=?$

As known, $l=a+( n-1)d$

$255=226+( n-1)1$

$\Rightarrow n-1=255-226$

$\Rightarrow n-1=29$

$\Rightarrow n=29+1=30$

The total no of numbers are $30$.