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

\(\sqrt{2}\) के प्रमाण में यदि (p) और (q) सहअभाज्य हैं, तो (p=2k) और (q=2r) मिलना क्यों असंभव है?

In the proof of \(\sqrt{2}\), if (p) and (q) are coprime, why is getting (p=2k) and (q=2r) impossible?

Explanation opens after your attempt
Correct Answer

A. क्योंकि दोनों में (2) साझा गुणनखंड होगाBecause both will have common factor (2)

Step 1

Concept

(p=2k) means (p) is even.

Step 2

Why this answer is correct

(q=2r) means (q) is also even.

Step 3

Exam Tip

Both have common factor (2), so they cannot be coprime. चरण 1: (p=2k) का अर्थ है (p) सम है। चरण 2: (q=2r) का अर्थ है (q) भी सम है। चरण 3: दोनों में (2) साझा गुणनखंड होगा, इसलिए वे सहअभाज्य नहीं रहेंगे।

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