The division of two irrational numbers is

1. a rational number
2. an irrational number
3. either a rational number or an irrational number
4. neither rational number nor irrational number

The division of two irrational numbers is either a rational number or an irrational number.

For example, let $2\sqrt{3}$ and $3\sqrt{3}$ be two irrational numbers.

$\dfrac{2\sqrt{3}}{3\sqrt{3}}$ = $\dfrac{2}{3}$ is rational number.

Let $2\sqrt{3}$ and $3\sqrt{5}$ be another two irrational numbers.

$\dfrac{2\sqrt{3}}{3\sqrt{5}}$ is an irrational number.

∴ Option 3, is the correct option.