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While proving the irrationality of (\sqrt{2}), if (\sqrt{2}=\frac{p}{q}) is assumed in lowest form, which reasoning from (p^2=2q^2) is most accurate?
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Answer and explanation
Correct answer: (p^2) is even, so (p) is even
Step 1: In (p^2=2q^2), the right side has factor (2), so (p^2) is even. Step 2: If the square of an integer is even, the integer is also even, so (p) is even. Step 3: Do not directly write (p=2q); first use divisibility.
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What is the correct answer to this question?
(p^2) is even, so (p) is even
Why is this the correct answer?
Step 1: In (p^2=2q^2), the right side has factor (2), so (p^2) is even. Step 2: If the square of an integer is even, the integer is also even, so (p) is even. Step 3: Do not directly write (p=2q); first use divisibility.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Proof of irrationality of √2, √3, √5.
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