If (a=3k) and (a^2=3b^2), what conclusion follows next?
Answer and explanation
Correct answer: \(b^2=3k^2\)
Substitute \(a=3k\) into \(a^2=3b^2\): \((3k)^2=3b^2\), so \(9k^2=3b^2\). Dividing both sides by 3 gives \(b^2=3k^2\). The option \(b^2=9k^2\) is incorrect because after division, the left side becomes \(3k^2\), not \(9k^2\). Exam tip: square the substituted value first, then simplify by dividing out common factors.
Frequently asked questions
What is the correct answer to this question?
\(b^2=3k^2\)
Why is this the correct answer?
Substitute \(a=3k\) into \(a^2=3b^2\): \((3k)^2=3b^2\), so \(9k^2=3b^2\). Dividing both sides by 3 gives \(b^2=3k^2\). The option \(b^2=9k^2\) is incorrect because after division, the left side becomes \(3k^2\), not \(9k^2\). Exam tip: square the substituted value first, then simplify by dividing out common factors.
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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