CBSE2026Class Class 10 · Mathematics1 Marks · Long✅ Verified
Assertion (A): $(\sqrt{3}+\sqrt{5})$ is an irrational number.
Reason (R): Sum of any two irrational numbers is always irrational.
Choose: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is not the correct explanation of A. (C) A is true but R is false. (D) A is false but R is true.
✅ Answer & Solution
Step 1: Check Assertion. $\sqrt3$ and $\sqrt5$ are irrational and $\sqrt3+\sqrt5$ cannot be written as $\dfrac{p}{q}$; it is irrational. Assertion is TRUE.
Step 2: Check Reason. Sum of two irrationals is NOT always irrational.
Step 3: Counter-example: $(2+\sqrt3)+(2-\sqrt3)=4$, which is rational. Also $\sqrt2+(-\sqrt2)=0$.
Step 4: So Reason is FALSE while Assertion is TRUE.
Answer: (C)
