Question

How many natural numbers are there in between $9^2$ and ${11}^2$?

• A. 37
• B. 36
• C. 38
• D. 39

Answer 1

The correct option is D

39

Total number of natural numbers between $n^2$ and $(n+1{)}^2$ is '2n'

Natural numbers between $9^2$ and ${10}^2$ $=2\times 9=18$

Natural numbers between ${10}^2$ and ${11}^2$ $=2\times 10=20$

Total natural numbers between $9^2$ and ${11}^2$

$=18+1+20=39$

$100={10}^2$ is counted as the extra number between $9^2$ and ${11}^2$.