If (p=3r) and (p^2=3q^2) then which relation is formed next?
Answer and explanation
Correct answer: \(q^2=3r^2\)
Substitute \(p=3r\) into \(p^2=3q^2\). This gives \((3r)^2=3q^2\), or \(9r^2=3q^2\). Dividing both sides by 3 gives \(q^2=3r^2\). Hence, option B is correct. There is no basis for \(q^2=2r^2\). Exam tip: while substituting, remember that \((3r)^2=9r^2\).
Frequently asked questions
What is the correct answer to this question?
\(q^2=3r^2\)
Why is this the correct answer?
Substitute \(p=3r\) into \(p^2=3q^2\). This gives \((3r)^2=3q^2\), or \(9r^2=3q^2\). Dividing both sides by 3 gives \(q^2=3r^2\). Hence, option B is correct. There is no basis for \(q^2=2r^2\). Exam tip: while substituting, remember that \((3r)^2=9r^2\).
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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