From (b^2=2k^2) what conclusion is obtained about (b)?
Answer and explanation
Correct answer: (b) is even
Since the right-hand side of (b^2=2k^2) is a multiple of 2, (b^2) is even. The square of an integer is even only when the integer itself is even; hence (b) is even. If (b) were odd, its square would also be odd, so option A is incorrect. Exam tip: in a contradiction proof of irrationality, this step helps show that both integers have the common factor 2.
Frequently asked questions
What is the correct answer to this question?
(b) is even
Why is this the correct answer?
Since the right-hand side of (b^2=2k^2) is a multiple of 2, (b^2) is even. The square of an integer is even only when the integer itself is even; hence (b) is even. If (b) were odd, its square would also be odd, so option A is incorrect. Exam tip: in a contradiction proof of irrationality, this step helps show that both integers have the common factor 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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