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

Assume (\sqrt{3}) is rational and (\sqrt{3}=\frac{a}{b}). If (a) and (b) are coprime, when will a contradiction occur in the proof?

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Answer and explanation

Correct answer: When both (a) and (b) are found divisible by (3)

Step 1: Coprime numbers have no common factor other than (1). Step 2: If both are divisible by (3), the common factor is (3). Step 3: This contradiction proves (\sqrt{3}) irrational.

Tags

sqrt3 proofcoprimecontradictionclass 10

Frequently asked questions

What is the correct answer to this question?

When both (a) and (b) are found divisible by (3)

Why is this the correct answer?

Step 1: Coprime numbers have no common factor other than (1). Step 2: If both are divisible by (3), the common factor is (3). Step 3: This contradiction proves (\sqrt{3}) 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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