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

After assuming (\sqrt{2}) rational, (\sqrt{2}=\frac{p}{q}) is written. If finally both (p) and (q) are even, what is the correct conclusion?

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Answer and explanation

Correct answer: (\sqrt{2}) is irrational

Step 1: (p) and (q) were assumed coprime at the start. Step 2: Both even shows common factor (2). Step 3: This is a contradiction, so (\sqrt{2}) is irrational.

Tags

sqrt2 conclusioncontradictionclass 10

Frequently asked questions

What is the correct answer to this question?

(\sqrt{2}) is irrational

Why is this the correct answer?

Step 1: (p) and (q) were assumed coprime at the start. Step 2: Both even shows common factor (2). Step 3: This is a contradiction, so (\sqrt{2}) 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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