Which type of number is the number $\pi$ - rational or irrational?

Rationalize the denominator of the following expression: $\frac{n^{2}}{\sqrt{m^{2}+n^{2}}+m}$

Simplify: $2^{-3} + (0.01)^{-\frac{1}{2}} - (27)^{\frac{2}{3}}$ (in $.125$)

Classify the following numbers as rational or irrational with justification:
$(i)$ $-\sqrt{0.4}$
$(ii)$ $\frac{\sqrt{12}}{\sqrt{75}}$

If $x = 3 + 2\sqrt{2}$,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 the four options given to make the statement true: $(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3}) = \ldots \ldots \ldots$