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Question Expert Mathematics Chapter 1: Real Numbers 6: Proof of irrationality of √2, √3, √5 Class 10 Level 16

\(\sqrt{5}\) की अपरिमेयता में (p) और (q) दोनों (5) से विभाज्य क्यों असंभव है?

Why is it impossible for both (p) and (q) to be divisible by (5) in the irrationality proof of \(\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

A. क्योंकि (p) और (q) सरलतम रूप में सहअभाज्य लिए गए थेBecause (p) and (q) were taken coprime in lowest form

Step 1

Concept

In lowest form, numerator and denominator are coprime.

Step 2

Why this answer is correct

Both being divisible by (5) gives a common factor.

Step 3

Exam Tip

So this situation goes against the starting condition. चरण 1: सरलतम रूप में अंश और हर सहअभाज्य होते हैं। चरण 2: दोनों का (5) से विभाज्य होना साझा गुणनखंड देता है। चरण 3: इसलिए यह स्थिति आरंभिक शर्त के विरुद्ध है।

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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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