If (p=2r) and (p^2=2q^2), which conclusion follows next?
Answer and explanation
Correct answer: \(q^2=2r^2\)
Given \(p=2r\), substitute it into \(p^2=2q^2\): \((2r)^2=2q^2\), so \(4r^2=2q^2\). Dividing both sides by 2 gives \(q^2=2r^2\). The result \(q^2=4r^2\) would come from incorrect division. Exam tip: after substitution, remember that \((2r)^2=4r^2\).
Frequently asked questions
What is the correct answer to this question?
\(q^2=2r^2\)
Why is this the correct answer?
Given \(p=2r\), substitute it into \(p^2=2q^2\): \((2r)^2=2q^2\), so \(4r^2=2q^2\). Dividing both sides by 2 gives \(q^2=2r^2\). The result \(q^2=4r^2\) would come from incorrect division. Exam tip: after substitution, remember that \((2r)^2=4r^2\).
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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