Prove that $\dfrac{1}{\sqrt{2}}$ is an irrational number.
Step-by-Step Solution
Key Concept: Assume $\dfrac{1}{\sqrt{2}} = \dfrac{a}{b} \Rightarrow \sqrt{2} = \dfrac{b}{a}$, contradiction.
Suppose $1/\sqrt{2} = a/b \Rightarrow \sqrt{2} = b/a$ (rational). [1.0 Mark]
Contradicts irrationality of $\sqrt{2}$. Hence $1/\sqrt{2}$ is irrational. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Reciprocating to $\sqrt{2} = b/a$: 1.0 Mark
Deducing contradiction: 1.0 Mark
Correct Answer: