Question

The rational number $\frac{3}{8}$ lies between which of the rational number ?

• A. $-\sqrt{2}$ and $\sqrt{2}$
• B. $\sqrt{3}$ and $\sqrt{5}$
• C. $\sqrt{7}$ and $\sqrt{11}$
• D. None of the above

Answer 1

The correct option is A $-\sqrt{2}$ and $\sqrt{2}$

Decimal value of $\frac{3}{8}$ is $0.375$.
Approximate values of $-\sqrt{2}$ and $\sqrt{2}$ is $-1.414$ and $1.414$ respectively.
So, $0.375$ lie between $-\sqrt{2}$ and $\sqrt{2}$.

Approximate values of $\sqrt{3}$ and $\sqrt{5}$ is $\mathrm{1.73...}$ and $\mathrm{2.23...}$ respectively.
So, $0.375$ doesn't lie between $\sqrt{3}$ and $\sqrt{5}$.

Approximate values of $\sqrt{7}$ and $\sqrt{11}$ is $\mathrm{2.64....}$ and $\mathrm{3.31...}$ respectively.
So, $0.375$ doesn't lie between $\sqrt{7}$ and $\sqrt{11}$.