Question

Total number of natural numbers between the following will be:

• A. 24
• B. 16
• C. 20
• D. 58

Answer 1

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

1. Natural numbers between $8^2$ and $9^2$ $=2\times 8=16$.

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

3. Natural numbers between ${12}^2$ and ${13}^2$ $=2\times 12=24$.

4. Natural numbers between ${14}^2$ and ${16}^2$ :
Natural numbers between ${14}^2$ and ${15}^2$ is $2\times 14=28$
and
Natural numbers between ${15}^2$ and ${16}^2$ is $2\times 15=30$

Considering ${15}^2=225$ as one natural number between ${14}^2$ and ${16}^2$

$\therefore$ Natural numbers between ${14}^2$ and ${16}^2$ is $28+1+30=59$