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

What is the contradiction in the proof of (\sqrt{3})?

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Answer and explanation

Correct answer: Both (p) and (q) are found divisible by (3)

Step 1: At the start, (p) and (q) are taken as coprime. Step 2: The proof shows both are divisible by (3), so they have common factor (3). Step 3: This contradiction proves (\sqrt{3}) is irrational.

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contradictionsqrt3 proofclass 10

Frequently asked questions

What is the correct answer to this question?

Both (p) and (q) are found divisible by (3)

Why is this the correct answer?

Step 1: At the start, (p) and (q) are taken as coprime. Step 2: The proof shows both are divisible by (3), so they have common factor (3). Step 3: This contradiction proves (\sqrt{3}) is irrational.

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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