Question

Is the product of a rational and an irrational number always irrational? Give an example.

Answer 1

Yes, the product of a rational and an irrational number is always an irrational number.
Example:
2 is a rational number and $\sqrt{3}$ is an irrational number.
Now, $2\times \sqrt{3}=2\sqrt{3}$, which is an irrational number.