Question

Product of two irrational number is always an irrational number.

• A. may be natural
• B. may be irrational

Answer 1

The correct option is B

may be irrational

Let the two irrational numbers be $a+\sqrt{b}$ and $a-\sqrt{b}$. [$b$ is not a perfect square]

Their product, $(a+\sqrt{b})(a-\sqrt{b})=a^2-(\sqrt{b}{)}^2=a^2-b$ which is rational.

So, the product of two irrational numbers need not necessarily be irrational.