Multiply $6 \sqrt{5}$ by $2 \sqrt{5}$.

Classify the following numbers as rational or irrational:
$(i)$ $2-\sqrt{5}$
$(ii)$ $(3+\sqrt{23})-\sqrt{23}$
$(iii)$ $\frac{2 \sqrt{7}}{7 \sqrt{7}}$
$(iv)$ $\frac{1}{\sqrt{2}}$
$(v)$ $2 \pi$

Visualize the representation of $5.3\overline{7}$ on the number line up to $5$ decimal places,that is,up to $5.37777$.

Locate $\sqrt{3}$ on the number line.

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

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