Question

Is the product of two irrationals always irrational? Justify your answer.

Answer 1

Product of two irrational numbers is not always an irrational number.
Example: $\sqrt{5}$ is irrational number. And $\sqrt{5}\times \sqrt{5}=5$ is a rational number. But the product of another two irrational numbers $\sqrt{2}\mathrm{and}\sqrt{3}$ is $\sqrt{6}$ which is also an irrational numbers.