Assertion (A): $(\sqrt{3} + \sqrt{5})$ is an irrational number.
Reason (R): Sum of any two irrational numbers is always irrational.
Select the correct answer from the options (A), (B), (C) and (D) as given below:
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
(C) Assertion (A) is true, but Reason (R) is false.
Assertion is true: $\sqrt{3}$ and $\sqrt{5}$ are both irrational, and their sum $(\sqrt{3}+\sqrt{5})$ is irrational. Reason is false: for example, $(\sqrt{3}) + (-\sqrt{3}) = 0$, which is rational. So the sum of two irrationals is not always irrational.
Source: Chapter 1, Section 1.3 – Revisiting Irrational Numbers
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Explanation
- A is true because $\sqrt{3}$ and $\sqrt{5}$ are proven irrationals (Section 1.3), and their sum cannot be rational (provable by contradiction).
- R is false because the statement "sum of any two irrationals is always irrational" has a counterexample: $\sqrt{3} + (-\sqrt{3}) = 0$ (rational). Examiners specifically look for this counterexample to disprove R.
- Since A is true but R is false, the answer is (C) — a very common trap in Assertion-Reason questions.