Question

How many numbers lie between squares of the following numbers?
$12$ and $13$
$99$ and $100$

• A. $24;198$
• B. $28;198$
• C. $24;192$
• D. $28;192$

Answer 1

The correct option is A $24;198$

1) Here, $n=12andn+1=13$.
$\because$ we know that between squares of $n^2$ and $(n+1{)}^2,2n$ non-perfect numbers lie.
Thus, between ${12}^{2}and{13}^2,2\times 12=24$ non-perfect square numbers lie.

2) Similarly, $2\times 99=198$ numbers lie between ${99}^{2}and{100}^2$.