Hard Mathematics Chapter 1: Real Numbers Class 10 Level 18

किस विकल्प में \(\sqrt{3}\) की अपरिमेयता सिद्ध करने के लिए उचित अंतिम वाक्य है?

Which option gives a proper final sentence for proving the irrationality of \(\sqrt{3}\)?

Explanation opens after your attempt
Correct Answer

A. अतः हमारी मान्यता गलत है, इसलिए \(\sqrt{3}\) अपरिमेय हैHence our assumption is false, so \(\sqrt{3}\) is irrational

Step 1

Concept

The proof reaches a contradiction from the rational assumption.

Step 2

Why this answer is correct

Once a contradiction is reached, the original assumption is false.

Step 3

Exam Tip

End clearly by stating that \(\sqrt{3}\) is irrational. चरण 1: प्रमाण में परिमेय मान्यता से विरोधाभास मिलता है। चरण 2: विरोधाभास मिलने पर प्रारंभिक मान्यता गलत होती है। चरण 3: अंत में साफ लिखें कि \(\sqrt{3}\) अपरिमेय है।

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The correct answer is A. अतः हमारी मान्यता गलत है, इसलिए \(\sqrt{3}\) अपरिमेय है / Hence our assumption is false, so \(\sqrt{3}\) is irrational.

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