Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:
$(i)$ $x^{2}=5$
$(ii)$ $y^{2}=9$
$(iii)$ $z^{2}=0.04$
$(iv)$ $u^{2}=\frac{17}{4}$

(A) $(i)$ $x^{2}=5 \Rightarrow x=\sqrt{5},$ which is an irrational number because $\sqrt{5}$ cannot be expressed in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$.
$(ii)$ $y^{2}=9 \Rightarrow y=\sqrt{9}=3,$ which is a rational number because it can be expressed as $\frac{3}{1}$.
$(iii)$ $z^{2}=0.04 \Rightarrow z=\sqrt{0.04}=0.2,$ which is a rational number because it is a terminating decimal and can be written as $\frac{2}{10} = \frac{1}{5}$.
$(iv)$ $u^{2}=\frac{17}{4} \Rightarrow u=\sqrt{\frac{17}{4}}=\frac{\sqrt{17}}{2}.$ Since $\sqrt{17}$ is not an integer,$u$ is an irrational number.