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

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

Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:
$(i)$ $x^{2}=5$
$(ii)$ $y^{2}=9$
$(iii)$ $z^{2}=0.04$
$(iv)$ $u^{2}=\frac{17}{4}$

Calculate the sum: $0.\overline{35} + 0.\overline{28}$.

Find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.

Simplify: $(256)^{4^{-\frac{3}{2}}}$