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

कौन सा विकल्प \(\sqrt{3}\) की सिद्धि में (p=3k) रखने के बाद सही आगे का तर्क देता है?

Which option gives the correct further reasoning after substituting (p=3k) in the proof of \(\sqrt{3}\)?

Explanation opens after your attempt
Correct Answer

A. \(9k^2=3q^2\), इसलिए \(q^2=3k^2\), अतः (q) (3) से विभाज्य है\(9k^2=3q^2\), so \(q^2=3k^2\), hence (q) is divisible by (3)

Step 1

Concept

If (p=3k), then \(p^2=9k^2\).

Step 2

Why this answer is correct

From \(9k^2=3q^2\), we get \(q^2=3k^2\).

Step 3

Exam Tip

By the prime rule, (q) is divisible by (3). चरण 1: (p=3k) रखने पर \(p^2=9k^2\) होगा। चरण 2: \(9k^2=3q^2\) से \(q^2=3k^2\) मिलता है। चरण 3: अभाज्य नियम से (q) (3) से विभाज्य होता है।

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