Question
Which one of the following statements is true?
(a) The sum of two irrational numbers is always an irrational number
(b) The sum of two irrational numbers is always a rational number
(c) The sum of two irrational numbers may be a rational number or an irrational number
(d) The sum of two irrational numbers is always an integer
Solution
Check with examples:
Case 1 (Irrational + Irrational = Rational):
\[ \sqrt{2} + (-\sqrt{2}) = 0 \quad (\text{rational}) \]
Case 2 (Irrational + Irrational = Irrational):
\[ \sqrt{2} + \sqrt{3} \quad (\text{irrational}) \]
Thus, the sum of two irrational numbers can be either rational or irrational.
Final Answer
✔ Correct option: (c)