State which of the following number(s) is/are irrational. $0.5$, $\frac{\pi}{2}$, $2\sqrt{2}$, $3\sqrt{3}\times\sqrt{3}$ Answer ...

1. Check which given numbers are rational or simplify to rational numbers

$0.5=\dfrac12$, so $0.5$ is rational.

$3\sqrt{3}\times\sqrt{3}=3\times 3=9$, so this is rational.

2. Identify the irrational numbers

$\dfrac{\pi}{2}$ is irrational since $\pi$ is irrational.

$2\sqrt{2}$ is irrational since $\sqrt{2}$ is irrational and multiplying by $2$ does not make it rational.