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Question Expert Mathematics Chapter 1: Real Numbers 6: Proof of irrationality of √2, √3, √5 Class 10 Level 18

\(\sqrt{5}\) के प्रमाण में \(a^2=5b^2\) से (a=5k) लिखने के लिए बीच का सही निष्कर्ष कौन-सा है?

In the proof for \(\sqrt{5}\), what is the correct intermediate conclusion needed to write (a=5k) from \(a^2=5b^2\)?

Explanation opens after your attempt
Correct Answer

B. \(5\mid a\)

Step 1

Concept

From \(a^2=5b^2\), we get \(5\mid a^2\).

Step 2

Why this answer is correct

Since (5) is prime, \(5\mid a\).

Step 3

Exam Tip

Then (a=5k) can be written. चरण 1: \(a^2=5b^2\) से \(5\mid a^2\) मिलता है। चरण 2: (5) अभाज्य होने से \(5\mid a\) निष्कर्ष मिलता है। चरण 3: फिर (a=5k) लिखा जा सकता है।

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