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

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

Find:
$(i)$ $2^{2/3} \cdot 2^{1/5}$
$(ii)$ $(1/3^3)^7$
$(iii)$ $11^{1/2} / 11^{1/4}$
$(iv)$ $7^{1/2} \cdot 8^{1/2}$

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

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

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?