Classify the following numbers as rational or irrational:
$(i)$ $\sqrt{23}$
$(ii)$ $\sqrt{225}$
$(iii)$ $0.3796$
$(iv)$ $7.478478 \ldots$
$(v)$ $1.101001000100001 \ldots$

(N/A) $(i)$ $\sqrt{23} \approx 4.79583152331 \ldots$
Since the decimal expansion is non-terminating and non-recurring,it is an irrational number.
$(ii)$ $\sqrt{225} = 15 = \frac{15}{1}$
Since it can be expressed in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$,it is a rational number.
$(iii)$ $0.3796 = \frac{3796}{10000} = \frac{949}{2500}$
Since the decimal expansion is terminating,it is a rational number.
$(iv)$ $7.478478 \ldots = 7.\overline{478}$
Since the decimal expansion is non-terminating but recurring,it is a rational number.
$(v)$ $1.101001000100001 \ldots$
Since the decimal expansion is non-terminating and non-repeating,it is an irrational number.