Question
Which of the following statements is true?
(a) Product of two irrational numbers is always irrational
(b) Product of a non-zero 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
Option (a)
✘ Incorrect
Example: \[ \sqrt{2} \times \sqrt{2} = 2 \quad (\text{rational}) \]
Option (b)
✔ Correct
Product of a non-zero rational number and an irrational number is always irrational.
Option (c)
✘ Incorrect
Example: \[ \sqrt{2} + \sqrt{3} \quad (\text{irrational}) \]
Option (d)
✘ Incorrect
Example: \[ 2 + 3 = 5 \quad (\text{integer}) \]
Final Answer
✔ Correct option: (b)