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Which option gives the correct short structure of the proof of (\sqrt{2})?कौन सा विकल्प (\sqrt{2}) की सिद्धि का सही संक्षिप्त ढांचा देता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Assume rational, square, find both even, contradict coprimeपरिमेय मानें, वर्ग करें, दोनों सम पाएं, सहअभाज्य से विरोधाभास
Step 1: Assume (\sqrt{2}) rational and write it as (\frac{p}{q}). Step 2: Squaring leads to both (p) and (q) being even. Step 3: Both even contradict the coprime condition.चरण 1: (\sqrt{2}) को परिमेय मानकर (\frac{p}{q}) लिखते हैं। चरण 2: वर्ग करने पर दोनों (p) और (q) सम निकलते हैं। चरण 3: दोनों सम होना सहअभाज्य शर्त से विरोधाभास देता है।
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