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Class 10MathematicsReal NumbersProof of irrationality of √2, √3, √5MediumLevel 18

In the proof of (\sqrt{3}), if both (p) and (q) are found divisible by (3), what does this contradict?

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Answer and explanation

Correct answer: Their being coprime

Step 1: Coprime numbers have no common factor except (1). Step 2: If both are divisible by (3), common factor (3) exists. Step 3: Therefore it contradicts the coprime condition.

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sqrt3 proofcontradictioncoprimeclass 10

Frequently asked questions

What is the correct answer to this question?

Their being coprime

Why is this the correct answer?

Step 1: Coprime numbers have no common factor except (1). Step 2: If both are divisible by (3), common factor (3) exists. Step 3: Therefore it contradicts 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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