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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5HardLevel 17

In the proof of (\sqrt{3}), which statement is correct but not the final conclusion?

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Answer and explanation

Correct answer: (p) is divisible by (3)

Step 1: From (p^2=3q^2), (p) is proved divisible by (3). Step 2: But to complete the proof, (q) must also be shown divisible by (3). Step 3: Only then does contradiction arise with the coprime condition.

Tags

sqrt3 proofincomplete conclusionhardclass 10

Frequently asked questions

What is the correct answer to this question?

(p) is divisible by (3)

Why is this the correct answer?

Step 1: From (p^2=3q^2), (p) is proved divisible by (3). Step 2: But to complete the proof, (q) must also be shown divisible by (3). Step 3: Only then does contradiction arise with 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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