Question

The product of any two irrational numbers

• A. Is always an irrational number
• B. Is always an rational number
• C. Is always an integer
• D. Can be rational or irrational number

Answer 1

The correct option is D

Can be rational or irrational number

Rational numbers are represented in $\frac{p}{q}$ form where $q$ is not equal to zero.

Irrational numbers are the numbers that cannot be represented as a simple fraction. It is a contradiction of rational numbers but is a type of real numbers.

Depending on the two numbers, the product of the two irrational numbers can be a rational or irrational number.

Example:

Consider $\sqrt{3}$ and $\sqrt{3}$ then

$\sqrt{3}$$\times$$\sqrt{3}$$=3$ It is a rational number.

Consider $\sqrt{3}$ and $\sqrt{2}$

$\sqrt{3}$ $\times$ $\sqrt{2}$$=\sqrt{6}$

It is an example of an irrational number.

Hence$,$ The product of any two irrational numbers can be rational or irrational number

Therefore$,$ option $\left(D\right)$ is correct.