Classify the following numbers as rational or irrational:
$(i)$ $2-\sqrt{5}$
$(ii)$ $(3+\sqrt{23})-\sqrt{23}$
$(iii)$ $\frac{2 \sqrt{7}}{7 \sqrt{7}}$
$(iv)$ $\frac{1}{\sqrt{2}}$
$(v)$ $2 \pi$

(N/A) $(i)$ $2-\sqrt{5}$: Since it is the difference between a rational number and an irrational number,it is an irrational number.
$(ii)$ $(3+\sqrt{23})-\sqrt{23} = 3+\sqrt{23}-\sqrt{23} = 3$. Since $3$ can be expressed as $\frac{3}{1}$,it is a rational number.
$(iii)$ $\frac{2 \sqrt{7}}{7 \sqrt{7}} = \frac{2}{7}$. Since this is in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$,it is a rational number.
$(iv)$ $\frac{1}{\sqrt{2}}$: The quotient of a rational number and an irrational number is always an irrational number. Therefore,it is an irrational number.
$(v)$ $2 \pi$: The product of a non-zero rational number and an irrational number is always an irrational number. Therefore,$2 \pi$ is an irrational number.