If (a=2k) and (a^2=2b^2) then which relation follows?
Answer and explanation
Correct answer: \(b^2=2k^2\)
Substituting \(a=2k\) into \(a^2=2b^2\) gives \((2k)^2=2b^2\), or \(4k^2=2b^2\). Dividing both sides by 2 gives \(b^2=2k^2\). The relation \(b^2=3k^2\) introduces an unjustified factor of 3, so it is incorrect. Exam tip: after substitution, expand the square first and then cancel common factors carefully.
Frequently asked questions
What is the correct answer to this question?
\(b^2=2k^2\)
Why is this the correct answer?
Substituting \(a=2k\) into \(a^2=2b^2\) gives \((2k)^2=2b^2\), or \(4k^2=2b^2\). Dividing both sides by 2 gives \(b^2=2k^2\). The relation \(b^2=3k^2\) introduces an unjustified factor of 3, so it is incorrect. Exam tip: after substitution, expand the square first and then cancel common factors carefully.
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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