Let $7\sqrt{5} = a/b$ (rational, $a, b \in \mathbb{Z}$). Then $\sqrt{5} = a/(7b)$. [1.0 Mark] Since $a/(7b)$ is rational, $\sqrt{5}$ would be rational, contradiction. Hence $7\sqrt{5}$ is irrational. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Isolating $\sqrt{5} = a/(7b)$: 1.0 Mark Deducing contradiction: 1.0 Mark
Correct Answer:
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