Divide $8 \sqrt{15}$ by $2 \sqrt{3}$.

Are the following statements true or false? Give reasons for your answers.
$(i)$ Every whole number is a natural number.
$(ii)$ Every integer is a rational number.
$(iii)$ Every rational number is an integer.

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

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

Find six rational numbers between $3$ and $4$.

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