Question
Which of the following is a correct statement?
(a) Sum of two irrational numbers is always irrational
(b) Sum of a rational and irrational number is always an irrational number
(c) Square of an irrational number is always a rational number
(d) Sum of two rational numbers can never be an integer
Solution
Option (a)
✘ Incorrect
Example: \[ \sqrt{2} + (-\sqrt{2}) = 0 \quad (\text{rational}) \]
Option (b)
✔ Correct
Sum of a rational number and an irrational number is always irrational.
Option (c)
✘ Incorrect
Example: \[ (\sqrt{2})^2 = 2 \quad (\text{rational}), \quad \text{but not always true} \]
Option (d)
✘ Incorrect
Example: \[ 2 + 3 = 5 \quad (\text{integer}) \]
Final Answer
✔ Correct option: (b)