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

In the proof of (\sqrt{5}), what does finding both (a) and (b) divisible by (5) show?

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Answer and explanation

Correct answer: They cannot be coprime

Step 1: If both are divisible by (5), both have (5) as a common factor. Step 2: This cannot happen for coprime numbers. Step 3: Thus the initial rational assumption becomes false.

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sqrt5 proofcontradictioncoprimeclass 10

Frequently asked questions

What is the correct answer to this question?

They cannot be coprime

Why is this the correct answer?

Step 1: If both are divisible by (5), both have (5) as a common factor. Step 2: This cannot happen for coprime numbers. Step 3: Thus the initial rational assumption becomes false.

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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