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If (p) and (q) are coprime positive integers and (\sqrt{3}=\frac{p}{q}) is assumed, what contradiction appears in the proof?
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Answer and explanation
Correct answer: Both (p) and (q) turn out divisible by (3)
Step 1: Assuming (\sqrt{3}=\frac{p}{q}) gives (p^2=3q^2). Step 2: This makes both (p) and (q) divisible by (3), contradicting that they are coprime. Step 3: In such proofs, finding a common factor creates the contradiction.
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What is the correct answer to this question?
Both (p) and (q) turn out divisible by (3)
Why is this the correct answer?
Step 1: Assuming (\sqrt{3}=\frac{p}{q}) gives (p^2=3q^2). Step 2: This makes both (p) and (q) divisible by (3), contradicting that they are coprime. Step 3: In such proofs, finding a common factor creates the contradiction.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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