Question

Which of the following numbers is irrational?

(a) $\sqrt{\frac{4}{8}}$

(b) $\frac{\sqrt{1250}}{\sqrt{8}}$

(c) $\sqrt{8}$

(d) $\frac{\sqrt{24}}{\sqrt{6}}$

Answer 1

$\left(a\right)\sqrt{\frac{4}{8}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}},irrational$

$\left(b\right)\frac{\sqrt{1250}}{\sqrt{8}}=\sqrt{\frac{1250}{8}}=\sqrt{\frac{625}{4}}=\frac{25}{2}rational$

$\left(c\right)\sqrt{8}=2\sqrt{2}irrational$

$\left(d\right)\frac{\sqrt{24}}{\sqrt{6}}=\sqrt{4}=2rational$

Answer a and c