Is the product of a rational and an irrational number always irrational?
Question:

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

Solution:

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.