$2 \sqrt{3} + \sqrt{3}$ is equal to

Add $4 \sqrt{3}+2 \sqrt{5}$ and $6 \sqrt{3}-4 \sqrt{5}$.

If $a = 2 + \sqrt{3}$,then find the value of $a - \frac{1}{a}$.

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

Simplify the following:
$3 \sqrt{3}+2 \sqrt{27}+\frac{7}{\sqrt{3}}$

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