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

State whether the following statements are true or false. Justify your answers.
$(i)$ Every irrational number is a real number.
$(ii)$ Every point on the number line is of the form $\sqrt{m}$,where $m$ is a natural number.
$(iii)$ Every real number is an irrational number.

Locate $\sqrt{2}$ on the number line.

Express $0.99999 \ldots$ in the form $\frac{p}{q}$. Are you surprised by your answer? With your teacher and classmates,discuss why the answer makes sense.

Show how $\sqrt{5}$ can be represented on the number line.

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