State whether the following statements are true or false? Justify your answer.
$(i)$ The square of an irrational number is always rational.
$(ii)$ $\frac{\sqrt{12}}{\sqrt{3}}$ is not a rational number as $\sqrt{12}$ and $\sqrt{3}$ are not integers.
Find five rational numbers between $\frac{2}{7}$ and $\frac{2}{5}$
Show that $0.142857142857 \ldots=\frac{1}{7}$
Simplify the following:
$(\sqrt{3}-\sqrt{2})^{2}$
Rationalise the denominator in each of the following
$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}}$