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Question Easy Mathematics Chapter 1: Real Numbers 6: Proof of irrationality of √2, √3, √5 Class 10 Level 17

कौन सा विकल्प \(\sqrt{2}\) के प्रमाण में विरोधाभास को सही भाषा में बताता है?

Which option states the contradiction in the proof of \(\sqrt{2}\) correctly?

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Correct Answer

A. (a) और (b) सहअभाज्य माने गए थे, पर दोनों सम निकले(a) and (b) were assumed coprime, but both turned out even

Step 1

Concept

At the beginning, \(\frac{a}{b}\) is taken in lowest form.

Step 2

Why this answer is correct

The proof shows both (a) and (b) are even.

Step 3

Exam Tip

Being coprime and both even is impossible. चरण 1: शुरुआत में \(\frac{a}{b}\) को सरलतम रूप मानते हैं। चरण 2: प्रमाण में (a) और (b) दोनों सम मिलते हैं। चरण 3: सहअभाज्य होकर दोनों सम होना असंभव है।

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