The product of a non-zero rational and an irrational number is:

The product of a non-zero rational and an irrational number is always irrational. For example:

$2\times \sqrt{3}$

$=2\sqrt{3}$

Here the product of 2 (rational number) and $\sqrt{3}$ (irrational number) is an irrational number $2\sqrt{3}$.