Rationalise the denominator of $\frac{1}{7+3 \sqrt{2}}$

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$?

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

Rationalise the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$.

Find the decimal expansions of $\frac{10}{3}$,$\frac{7}{8}$ and $\frac{1}{7}$.

Simplify each of the following expressions:
$(i)$ $(3+\sqrt{3})(2+\sqrt{2})$
$(ii)$ $(3+\sqrt{3})(3-\sqrt{3})$
$(iii)$ $(\sqrt{5}+\sqrt{2})^{2}$
$(iv)$ $(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$