Question

The product of any two irrational numbers is:

• A. always an irrational number
• B. always a rational number
• C. always an integer
• D. Sometimes rational, sometimes irrational.

Answer 1

The correct option is D

Sometimes rational, sometimes irrational.

Irrational number:

An irrational number is a number that can not be represented in the form of $\frac{p}{q}$ where $q$ is not equal to 0.

Example: Consider $\sqrt{2}\mathrm{and}\sqrt{2}$ then,

$\sqrt{2}\times \sqrt{2}=2$

It is a rational number.

Now, consider $\sqrt{5}\mathrm{and}\sqrt{6}$then,

$\sqrt{5}\times \sqrt{6}=\sqrt{30}$

It is an irrational number.

Thus, the product of any two irrational numbers is sometimes rational, sometimes irrational. It totally depends on the numbers.

Hence, option D is correct.