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

Classify the following numbers as rational or irrational :

$(i)$ $2-\sqrt{5}$

$(ii)$ $(3+\sqrt{23})-\sqrt{23}$

$(iii)$ $\frac{2 \sqrt{7}}{7 \sqrt{7}}$

$(iv)$ $\frac{1}{\sqrt{2}}$

$(v)$ $2 \pi$

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

Locate $\sqrt 2$ on the number line.

Visualise $4. \overline{26}$ . on the number line, up to $4$ decimal places.

Find :

$(i)$ $9^{\frac{3}{2}}$

$(ii)$ $32^{\frac{2}{5}}$

$(iii)$ $16^{\frac{3}{4}}$

$(iv)$ $125^{\frac{-1}{3}}$