The product of a non-zero rational number and an irrational number is:
(a) Always irrational
(b) Always rational
(c) Rational or irrational
(d) One
Step-by-Step Solution
Key Concept: If $r <br>eq 0$ is rational and $x$ is irrational, $r \cdot x$ cannot be rational.
If $r \cdot x = q \in \mathbb{Q}$, then $x = q/r \in \mathbb{Q}$, contradiction. Hence product is always irrational. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Contradiction proof recall: 1.0 Mark
Correct Answer: Always irrational