Question

The product of two irrational numbers is

• A. Always irrational
• B. Always rational
• C. Can be both rational or irrational
• D. always an integer

Answer 1

The correct option is C Can be both rational or irrational

According to the properties of irrational numbers, the product of two irrational numbers can be both rational or irrational.

For example, let $p=\sqrt{3}$ and $q=\sqrt{3}$ be two irrational numbers
$\therefore pq=\sqrt{3}\times \sqrt{3}=3$
Here, $3$ is a rational number.

Now, let $p=\sqrt{3}$ and $q=\sqrt{2}$
$\therefore pq=\sqrt{3}\times \sqrt{2}=\sqrt{6}$
Here, $\sqrt{6}$ is an irrational number.

Hence, the product can be both rational or irrational.
So, option C is correct.