Is the product of two irrationals always irrational? Justify your… - Vidyadip

Question

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

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Answer

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 $\sqrt{2}$ and $\sqrt{3}$ is $\sqrt{6}$ which is also an irrational numbers.

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