Simplify the following expression: $(\sqrt{15}+\sqrt{7})(\sqrt{15}-\sqrt{7})$

Rationalise the denominator in each of the following:
$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}}$

Find the value of $\sqrt[5]{(243)^{-3}}$.

Rationalise the denominator of the following number:
$\frac{1}{5+2 \sqrt{3}}$

State whether the following statement is true or false. Justify your answer.
$\frac{\sqrt{15}}{\sqrt{3}}$ is written in the form $\frac{p}{q},$ where $q \neq 0,$ so it is a rational number.

State whether the following statement is true or false:
Every whole number is a rational number.