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

Locate $\sqrt{3}$ on the number line.

Visualize $4.\overline{26}$ on the number line,up to $4$ decimal places.

Rationalise the denominators of the following:
$(i)$ $\frac{1}{\sqrt{7}}$
$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$
$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$
$(iv)$ $\frac{1}{\sqrt{7}-2}$

Show that $1.272727 \ldots = 1.\overline{27}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

Write the following in decimal form and state what kind of decimal expansion each has:
$(i)$ $\frac{36}{100}$
$(ii)$ $\frac{1}{11}$
$(iii)$ $4 \frac{1}{8}$
$(iv)$ $\frac{3}{13}$
$(v)$ $\frac{2}{11}$
$(vi)$ $\frac{329}{400}$