From (q^2=2r^2) what conclusion follows about (q)?
Answer and explanation
Correct answer: (q) is even
In (q^2=2r^2), the right-hand side is a multiple of 2, so (q^2) is even. The square of an integer is even only when the integer itself is even; hence, (q) is even. Being prime, negative, or zero does not necessarily follow from this equation. Exam tip: Remember: an even square implies an even integer.
Frequently asked questions
What is the correct answer to this question?
(q) is even
Why is this the correct answer?
In (q^2=2r^2), the right-hand side is a multiple of 2, so (q^2) is even. The square of an integer is even only when the integer itself is even; hence, (q) is even. Being prime, negative, or zero does not necessarily follow from this equation. Exam tip: Remember: an even square implies an even integer.
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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