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

If assuming (\sqrt{3}) rational makes both (p) and (q) divisible by (3), which fact is proved false?

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Answer and explanation

Correct answer: (p) and (q) are coprime

Step 1: Coprime numbers have no common factor except (1). Step 2: If both are divisible by (3), they have common factor (3). Step 3: Thus the assumption of being coprime breaks.

Tags

sqrt3 proofcoprimecontradictionclass 10

Frequently asked questions

What is the correct answer to this question?

(p) and (q) are 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), they have common factor (3). Step 3: Thus the assumption of being coprime breaks.

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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