किस विकल्प में \(\sqrt{2}\) के प्रमाण का सही निष्कर्ष और कारण है?

Which option gives the correct conclusion and reason for the proof of \(\sqrt{2}\)?

Author: Muft Shiksha Editorial Team Published:
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Correct Answer

A. अपरिमेय क्योंकि परिमेय मान्यता से दोनों सम मिलते हैंIrrational because rational assumption makes both even

Step 1

Concept

Both becoming even contradicts the coprime condition. Therefore \(\sqrt{2}\) is irrational.

Step 2

Why this answer is correct

The correct answer is A. अपरिमेय क्योंकि परिमेय मान्यता से दोनों सम मिलते हैं / Irrational because rational assumption makes both even. Both becoming even contradicts the coprime condition. Therefore \(\sqrt{2}\) is irrational.

Step 3

Exam Tip

दोनों सम मिलना सहभाज्य शर्त से विरोधाभास देता है। इसलिए \(\sqrt{2}\) अपरिमेय है।

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Mathematics Answer, Explanation and Revision Hints

किस विकल्प में \(\sqrt{2}\) के प्रमाण का सही निष्कर्ष और कारण है? / Which option gives the correct conclusion and reason for the proof of \(\sqrt{2}\)?

Correct Answer: A. अपरिमेय क्योंकि परिमेय मान्यता से दोनों सम मिलते हैं / Irrational because rational assumption makes both even. Explanation: दोनों सम मिलना सहभाज्य शर्त से विरोधाभास देता है। इसलिए \(\sqrt{2}\) अपरिमेय है। / Both becoming even contradicts the coprime condition. Therefore \(\sqrt{2}\) is irrational.

Which concept should I revise for this Mathematics MCQ?

Both becoming even contradicts the coprime condition. Therefore \(\sqrt{2}\) is irrational.

What exam hint can help solve this Mathematics question?

दोनों सम मिलना सहभाज्य शर्त से विरोधाभास देता है। इसलिए \(\sqrt{2}\) अपरिमेय है।