Question:
Which of the following numbers is irrational?
(a) $\sqrt{\frac{4}{9}}$
(b) $\frac{\sqrt{1250}}{\sqrt{8}}$
(c) $\sqrt{8}$
(d) $\frac{\sqrt{24}}{\sqrt{6}}$
Solution:
Since,
$\sqrt{\frac{4}{9}}=\frac{2}{3}$, which is a rational number,
$\frac{\sqrt{1250}}{\sqrt{8}}=\sqrt{\frac{1250}{8}}=\sqrt{\frac{625}{4}}=\frac{25}{2}$, which is a rational number,
$\sqrt{8}=2 \sqrt{2}$, which is an irrational number, and
$\frac{\sqrt{24}}{\sqrt{6}}=\sqrt{\frac{24}{6}}=\sqrt{4}=2$, which is a rational number
Hence, the correct option is (c).