The product of any two irrational numbers is

1. always an irrational number
2. always a rational number
3. always an integer
4. sometimes rational, sometimes irrational

The product of any two irrational numbers is sometimes rational, sometimes irrational

For example, $2\sqrt{3}$ and $3\sqrt{3}$ are two irrational number .

Their product $2\sqrt{3}$ × $3\sqrt{3}$ = 6 × $(\sqrt{3})^2$ = 6 × 3 = 18 which is rational number.

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

Their product $2\sqrt{2}$ × $3\sqrt{3}$ = 6 × $\sqrt{2}$ × $\sqrt{3}$ = $6\sqrt{6}$ which is an irrational number.

∴ Option 4, is the correct option.