If (r=3t) and (r^2=3s^2), what follows next?
Answer and explanation
Correct answer: \(s^2=3t^2\)
Given \(r=3t\), substitute it into \(r^2=3s^2\). This gives \((3t)^2=3s^2\), or \(9t^2=3s^2\). Dividing both sides by 3 gives \(s^2=3t^2\). Hence, option C is correct. \(t=0\) does not necessarily follow. Exam tip: After substitution, square the expression correctly and then simplify the coefficients.
Frequently asked questions
What is the correct answer to this question?
\(s^2=3t^2\)
Why is this the correct answer?
Given \(r=3t\), substitute it into \(r^2=3s^2\). This gives \((3t)^2=3s^2\), or \(9t^2=3s^2\). Dividing both sides by 3 gives \(s^2=3t^2\). Hence, option C is correct. \(t=0\) does not necessarily follow. Exam tip: After substitution, square the expression correctly and then simplify the coefficients.
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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