Which statement is a wrong conclusion in the proof of \(\sqrt{3}\)?
Answer and explanation
Correct answer: Even if both \(p\) and \(q\) are divisible by \(3\), they are coprime
If both \(p\) and \(q\) are divisible by \(3\), then they have \(3\) as a common factor. Hence, they cannot be coprime. In the irrationality proof of \(\sqrt{3}\), \(p\) and \(q\) are assumed to be coprime; showing that both are divisible by \(3\) gives the required contradiction. Therefore, option C is the wrong conclusion. Exam tip: coprime numbers always have HCF \(1\).
Frequently asked questions
What is the correct answer to this question?
Even if both \(p\) and \(q\) are divisible by \(3\), they are coprime
Why is this the correct answer?
If both \(p\) and \(q\) are divisible by \(3\), then they have \(3\) as a common factor. Hence, they cannot be coprime. In the irrationality proof of \(\sqrt{3}\), \(p\) and \(q\) are assumed to be coprime; showing that both are divisible by \(3\) gives the required contradiction. Therefore, option C is the wrong conclusion. Exam tip: coprime numbers always have HCF \(1\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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