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

Which opening sentence is most complete for proving the irrationality of (\sqrt{2})?

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Answer and explanation

Correct answer: Assume (\sqrt{2}=\frac{p}{q}), where (p,q) are coprime integers and (q\neq0)

Step 1: A rational number is written as a ratio of two integers. Step 2: The denominator cannot be zero, and the ratio should be in lowest form. Step 3: This complete opening sentence sets the proof correctly.

Tags

real-numbersroot2opening-statementrational-form

Frequently asked questions

What is the correct answer to this question?

Assume (\sqrt{2}=\frac{p}{q}), where (p,q) are coprime integers and (q\neq0)

Why is this the correct answer?

Step 1: A rational number is written as a ratio of two integers. Step 2: The denominator cannot be zero, and the ratio should be in lowest form. Step 3: This complete opening sentence sets the proof correctly.

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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