# An irrational number between

Question:

An irrational number between $\frac{1}{7}$ and $\frac{2}{7}$ is

(a) $\frac{1}{2}\left(\frac{1}{7}+\frac{2}{7}\right)$

(b) $\left(\frac{1}{7} \times \frac{2}{7}\right)$

(c) $\sqrt{\frac{1}{7} \times \frac{2}{7}}$

(d) none of these

Solution:

(c) $\sqrt{\frac{1}{7} \times \frac{2}{7}}$

An irrational number between $a$ and $b$ is given as $\sqrt{a b}$.