Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers:

$(i)$ $x^{2}=5$

$(ii)$ $\quad y^{2}=9$

$(iii)$ $z^{2}=.04$

$(iv)$ $u^{2}=\frac{17}{4}$

$(i)$ $x^{2}=5 \Rightarrow x=\sqrt{5},$ which is an irrational number.

$(ii)$ $y^{2}=9 \Rightarrow y=\sqrt{9}=3,$ which is a rational number.

$(iii)$ $z^{2}=.04 \Rightarrow z=\sqrt{.04}=0.2,$ which is a terminating decimal.

Hence, it is rational number.

$(iv)$ $u^{2}=\frac{17}{4} \Rightarrow u=\sqrt{\frac{17}{4}}=\frac{\sqrt{17}}{2},$ which is of the form $\frac{p}{q},$ where $p=\sqrt{17}$ is not an integer.

Hence, u is an irrational number.