Divide $12 \sqrt{30}$ by $3 \sqrt{5}$.

Classify the following numbers as rational or irrational with justification:
$(i)$ $\sqrt{\frac{9}{27}}$
$(ii)$ $\frac{\sqrt{28}}{\sqrt{343}}$

If $x = 5 + 2\sqrt{6}$,then find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{3} + \frac{1}{x^{3}}$.

For each question,select the proper option from four options given,to make the statement true: $\sqrt{5} \times \sqrt{5}$ is a / an $\ldots \ldots \ldots$ number.

Simplify: $(256)^{4^{-\frac{3}{2}}}$

Find three rational numbers between $0.1$ and $0.11$.