Simplify the following:
$4 \sqrt{28} \div 3 \sqrt{7}$

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

If $\frac{5+3 \sqrt{3}}{7+4 \sqrt{3}}=a+b \sqrt{3},$ find the value of $a$ and $b$.

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 $\sqrt{5} = 2.236$.
$\frac{1}{\sqrt{3} + \sqrt{2}}$

Rationalise the denominator of the following expression and evaluate it by taking $\sqrt{3} = 1.732$,up to three decimal places:
$\frac{4}{\sqrt{3}}$

Rationalise the denominator of the following:
$\frac{16}{\sqrt{41}-5}$