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If (\sqrt{2}) is assumed rational and written as (\sqrt{2}=\frac{p}{q}), where (p) and (q) are coprime, where does the contradiction mainly come from?
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Answer and explanation
Correct answer: (p) and (q) both become even
Step 1: Assuming (\sqrt{2}=\frac{p}{q}) gives (p^2=2q^2). Step 2: So (p^2) is even, hence (p) is even, and then (q) also becomes even. Step 3: In exams, remember that coprime numbers cannot both be even.
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What is the correct answer to this question?
(p) and (q) both become even
Why is this the correct answer?
Step 1: Assuming (\sqrt{2}=\frac{p}{q}) gives (p^2=2q^2). Step 2: So (p^2) is even, hence (p) is even, and then (q) also becomes even. Step 3: In exams, remember that coprime numbers cannot both be even.
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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