\(\sqrt{2}\) के प्रमाण में कौन-सा कथन सही कारण और निष्कर्ष दोनों देता है?
Which statement gives both correct reason and conclusion in the proof of \(\sqrt{2}\)?
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Correct Answer
A. परिमेय मान्यता से (m,n) दोनों सम निकलते हैं इसलिए \(\sqrt{2}\) अपरिमेय हैRational assumption makes both (m,n) even, so \(\sqrt{2}\) is irrational
Concept
Both even contradicts the lowest coprime fraction. This proves irrationality.
Why this answer is correct
The correct answer is A. परिमेय मान्यता से (m,n) दोनों सम निकलते हैं इसलिए \(\sqrt{2}\) अपरिमेय है / Rational assumption makes both (m,n) even, so \(\sqrt{2}\) is irrational. Both even contradicts the lowest coprime fraction. This proves irrationality.
Exam Tip
दोनों सम होना सरलतम सहभाज्य भिन्न से विरोधाभास है। यही अपरिमेयता सिद्ध करता है।
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