Multiply $3 \sqrt{7}$ and $5 \sqrt{7}$.

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

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

Rationalise the denominator of the following:
$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$

Simplify the following expression: $(3+\sqrt{5})(4-\sqrt{11})$

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Given $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{1}{\sqrt{3} + \sqrt{2}}$