Medium Mathematics Chapter 1: Real Numbers Class 10 Level 18

यदि \(p^2=2q^2\) से (p=2k) और फिर (q=2r) मिलते हैं, तो यह कौन सा प्रमाण पूरा करता है?

If from \(p^2=2q^2\), (p=2k) and then (q=2r) are obtained, which proof does this complete?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\) की अपरिमेयताIrrationality of \(\sqrt{2}\)

Step 1

Concept

In \(p^2=2q^2\), the key factor is (2).

Step 2

Why this answer is correct

Finding both (p) and (q) divisible by (2) identifies the proof of \(\sqrt{2}\).

Step 3

Exam Tip

This gives contradiction to the coprime condition. चरण 1: \(p^2=2q^2\) में मुख्य गुणनखंड (2) है। चरण 2: (p) और (q) दोनों (2) से विभाज्य मिलना \(\sqrt{2}\) के प्रमाण की पहचान है। चरण 3: इससे सहअभाज्य शर्त से विरोधाभास आता है।

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The correct answer is A. \(\sqrt{2}\) की अपरिमेयता / Irrationality of \(\sqrt{2}\).

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