Question

Which of the following rational number lie between $\sqrt{2}$ and $\sqrt{5}$.

• A. $\frac{1}{2}$
• B. $\frac{8}{5}$
• C. $\frac{7}{2}$
• D. All of the above.

Answer 1

The correct option is B $\frac{8}{5}$

Approximate value of $\sqrt{2}=\mathrm{1.414...}$ and that of $\sqrt{5}=\mathrm{2.234....}$

$\text{Option (a)}\frac{1}{2}=0.5<\mathrm{1.414....}$
hence, it does not lie between $\sqrt{2}$ and $\sqrt{5}$.

$\text{Option (c)}\frac{7}{2}=3.5>\mathrm{2.234....}$
hence, it doesn't lie between $\sqrt{2}$ and $\sqrt{5}$

$\text{Option (b)}\frac{8}{5}=1.6$
here, $\mathrm{1.414....}<1.6<\mathrm{2.234...}$
Hence, it lies between $\sqrt{2}$ and $\sqrt{5}$.