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

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :

$0.2555 \ldots$

If $2^{x-2} \cdot 3^{2 x-6}=36,$ then find $x$.

Insert a rational number and an irrational number between the following:

$\frac{-2}{5}$ and $\frac{1}{2}$

A rational number between $\sqrt{2}$ and $\sqrt{3}$ is

Simplify the following:

$\frac{2 \sqrt{3}}{3}-\frac{\sqrt{3}}{6}$