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

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 $\sqrt{5} = 2.236$.
$\frac{4}{3 \sqrt{3}-2 \sqrt{2}} + \frac{3}{3 \sqrt{3}+2 \sqrt{2}}$

State whether the following statement is true or false:
$(-1)^{11} = -1$

The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ equals

Represent $\sqrt{6}$ on the number line.

Classify the following numbers as rational or irrational with justification:
$(i)$ $10.124124 \ldots$
$(ii)$ $1.010010001 \ldots$