Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$

(N/A) $(i)$ $-\sqrt{0.4} = -\sqrt{\frac{4}{10}} = -\frac{2}{\sqrt{10}}$. Since $\sqrt{10}$ is an irrational number,the quotient of a rational number $(2)$ and an irrational number $(\sqrt{10})$ is irrational. Therefore,$-\sqrt{0.4}$ is an irrational number.
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}} = \sqrt{\frac{12}{75}} = \sqrt{\frac{4}{25}} = \frac{2}{5}$. Since $\frac{2}{5}$ is in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$,it is a rational number.