Divide $12 \sqrt{30}$ by $3 \sqrt{5}$.

Represent $3.\overline{42}$ on the number line, using successive magnification, up to $4$ decimal places.

Represent the number $\sqrt{5.6}$ geometrically on the number line.

Let $x$ and $y$ be rational and irrational numbers,respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.

Rationalize the denominator of the following expression: $\frac{n^{2}}{\sqrt{m^{2}+n^{2}}+m}$

Rationalise the denominator in each of the following:
$\frac{1}{7-4 \sqrt{3}}$