Question

Total natural numbers lying between squares of $99$ and $100$

Answer 1

Let's find the number of natural numbers between squares of $99$ and $100$.

The total natural numbers lying between squares of $99$ and $100$ is $198$.

The total numbers of natural number between two square terms is given as

Let the numbers $a^2$ and $b^2$

The total numbers are $n=a+b-1$

$a=99$ and $b=100$

Applying in equation $n=a+b-1$

$$\begin{gathered} n=99+100-1 \\ n=199-1 \\ n=198. \end{gathered}$$

Hence the answer is $198$.