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

You know that $\frac{1}{7} = 0.\overline{142857}$. Can you predict what the decimal expansions of $\frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}$ are,without actually doing the long division? If so,how?

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

Show that $0.3333... = 0.\overline{3}$ can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.

Show that $3.142678$ is a rational number. In other words,express $3.142678$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \ne 0$.

Find the values of:
$(i)$ $64^{\frac{1}{2}}$
$(ii)$ $32^{\frac{1}{5}}$
$(iii)$ $125^{\frac{1}{3}}$