In the proof of \(\sqrt{2}\), what is the first conclusion after getting \(a^2=2b^2\)?
Answer and explanation
Correct answer: \(a^2\) is even
In \(a^2=2b^2\), the right-hand side is a multiple of \(2\), so \(a^2\) is even. The next step is to conclude that \(a\) is also even. We cannot conclude at this stage that \(b\) is odd. Exam tip: In such proofs, first compare the parity of both sides of the equation.
Frequently asked questions
What is the correct answer to this question?
\(a^2\) is even
Why is this the correct answer?
In \(a^2=2b^2\), the right-hand side is a multiple of \(2\), so \(a^2\) is even. The next step is to conclude that \(a\) is also even. We cannot conclude at this stage that \(b\) is odd. Exam tip: In such proofs, first compare the parity of both sides of the equation.
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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