Which option gives the correct squared relation used in the proof of \(\sqrt{2}\)?
Answer and explanation
Correct answer: If \(\sqrt{2}=\frac{m}{n}\), then \(m^2=2n^2\)
Assume that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are integers and \(n\ne0\). Squaring both sides gives \(2=\frac{m^2}{n^2}\). Multiplying by \(n^2\) gives \(m^2=2n^2\), so option A is correct. Option B, with \(3n^2\), is the corresponding relation for \(\sqrt{3}\), not for \(\sqrt{2}\). Exam tip: for a square-root fraction relation, square both sides first and then clear the denominator.
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What is the correct answer to this question?
If \(\sqrt{2}=\frac{m}{n}\), then \(m^2=2n^2\)
Why is this the correct answer?
Assume that \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are integers and \(n\ne0\). Squaring both sides gives \(2=\frac{m^2}{n^2}\). Multiplying by \(n^2\) gives \(m^2=2n^2\), so option A is correct. Option B, with \(3n^2\), is the corresponding relation for \(\sqrt{3}\), not for \(\sqrt{2}\). Exam tip: for a square-root fraction relation, square both sides first and then clear the denominator.
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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