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

कौन सा विकल्प \(\sqrt{2}\) की सिद्धि का सही अंतिम वाक्य है?

Which option is the correct final sentence of the proof of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. यह हमारी मान्यता के विपरीत है, अतः \(\sqrt{2}\) अपरिमेय हैThis contradicts our assumption, hence \(\sqrt{2}\) is irrational

Step 1

Concept

The rational assumption makes both (p) and (q) even.

Step 2

Why this answer is correct

This contradicts their being coprime.

Step 3

Exam Tip

So the final sentence should state both contradiction and irrationality. चरण 1: परिमेय मान्यता से (p) और (q) दोनों सम मिलते हैं। चरण 2: यह सहअभाज्य होने के विरुद्ध है। चरण 3: इसलिए अंतिम वाक्य में विरोधाभास और अपरिमेयता दोनों लिखें।

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