State the number which is a whole number but not a natural number.

Find four rational numbers between $\frac{2}{9}$ and $\frac{2}{7}$.

If $a = \frac{3+\sqrt{5}}{2}$,then find the value of $a^{2} + \frac{1}{a^{2}}$.

Find the value of $64^{\frac{5}{6}}$.

If $a = 5 + 2\sqrt{6}$ and $b = \frac{1}{a}$,then what will be the value of $a^2 + b^2$?

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