Simplify the following expressions

$(3+\sqrt{5})(4-\sqrt{11})$

Find the values of each of the following correct to three places of decimals, rationalising the denominator if needed and taking $\sqrt{2}=1.414$ $\sqrt{3}=1.732$ and $\sqrt{5}=2.236$

$\frac{4}{3 \sqrt{3}-2 \sqrt{2}}+\frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:

$(i)$ $x^{2}=5$

$(ii)$ $\quad y^{2}=9$

$(iii)$ $z^{2}=.04$

$(iv)$ $u^{2}=\frac{17}{4}$

Find three different irrational numbers between the rational numbers $\frac{1}{4}$ and $\frac{4}{5}$.

Find the value

$625^{\frac{3}{4}}$

Rationalise the denominator of the following:

$\frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}}$