Question

Which of the following is a true statement?

• A. The sum of two irrational numbers is an irrational number
• B. The product of two irrational numbers is an irrational number
• C. Every real number is always rational
• D. Every real number is either rational or irrational

Answer 1

The correct option is D Every real number is either rational or irrational

Take 2 irrational numbers, $\sqrt{3}$, $(-\sqrt{3})$. Their sum will be equal to $0$ which is a rational number. Hence the sum of 2 irrational numbers is not always an irrational number.
The product of $3\sqrt{2}\times \sqrt{2}=6$, which is a rational number.
Every real number can be said to be a rational number but not the converse.
Both rational and irrational numbers fall in the category of real numbers.