Question

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

(a) always rational
(b) always irrational
(c) rational of irrational
(d) 1

Answer 1

(b) always irrational
Product of non-zero rational and an irrational number is always an irrational.
For example, let 2 and $\sqrt{2}$ be rational and an irrational number such that their product is $2\times \sqrt{2}=2\sqrt{2}$, which is an irrational number.