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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5EasyLevel 16

What correct conclusion is obtained by putting (p=3k) in (p^2=3q^2)?

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Answer and explanation

Correct answer: (q^2=3k^2), so (q) is divisible by (3)

Step 1: Putting (p=3k) gives (p^2=9k^2). Step 2: From (9k^2=3q^2), we get (q^2=3k^2), so (q) is also divisible by (3). Step 3: A common factor breaks the coprime condition.

Tags

substitutionsqrt3 proofclass 10

Frequently asked questions

What is the correct answer to this question?

(q^2=3k^2), so (q) is divisible by (3)

Why is this the correct answer?

Step 1: Putting (p=3k) gives (p^2=9k^2). Step 2: From (9k^2=3q^2), we get (q^2=3k^2), so (q) is also divisible by (3). Step 3: A common factor breaks the coprime condition.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.

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