If (m=2k) and (m^2=2n^2), which relation follows?
Answer and explanation
Correct answer: \(n^2=2k^2\)
Given \(m=2k\), substitute it into \(m^2=2n^2\). This gives \((2k)^2=2n^2\), or \(4k^2=2n^2\). Dividing both sides by 2, we get \(n^2=2k^2\). Hence, option B is correct. In \(n^2=k^2\), the factor 2 has been incorrectly omitted. Exam tip: when substituting a term that is squared, square its coefficient as well.
Frequently asked questions
What is the correct answer to this question?
\(n^2=2k^2\)
Why is this the correct answer?
Given \(m=2k\), substitute it into \(m^2=2n^2\). This gives \((2k)^2=2n^2\), or \(4k^2=2n^2\). Dividing both sides by 2, we get \(n^2=2k^2\). Hence, option B is correct. In \(n^2=k^2\), the factor 2 has been incorrectly omitted. Exam tip: when substituting a term that is squared, square its coefficient as well.
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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