# Which of the following statements is true?

Question:

Which of the following statements is true?
(a) Product of two irrational numbers is always irrational
(b) Product of a rational and an irrational number is always irrational
(c) Sum of two irrational numbers can never be irrational
(d) Sum of an integer and a rational number can never be an integer

Solution:

Since we know that the product of rational and irrational number is always an irrational. For example: Let $\frac{1}{2}, \sqrt{3}$ are rational and irrational numbers respectively and their product is $\frac{\sqrt{3}}{2}$

Hence the correct option is $b$.