Express $0.\overline{83}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.

Find three different irrational numbers lying between $\sqrt{3}$ and $\sqrt{5}$.

Find the value of the following expression correct to three decimal places,rationalizing the denominator if needed. Take $\sqrt{2} = 1.414$,$\sqrt{3} = 1.732$,and $\sqrt{5} = 2.236$.
$\frac{\sqrt{2}}{2+\sqrt{2}}$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.00323232 \ldots$

Simplify: $5 \sqrt{2} + 2 \sqrt{8} - 3 \sqrt{32} + 4 \sqrt{128}$ (in $\sqrt{2}$)

If $\sqrt{2}=1.414$ and $\sqrt{3}=1.732,$ find the value of $\frac{4}{3\sqrt{3}-2\sqrt{2}}+\frac{3}{3\sqrt{3}+2\sqrt{2}}.$