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Why is the assumption (\sqrt{3}=\frac{m}{n}) finally proved wrong when (m,n) are taken coprime?
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Answer and explanation
Correct answer: (m) and (n) both turn out divisible by (3)
Step 1: From (\sqrt{3}=\frac{m}{n}), we get (m^2=3n^2). Step 2: This leads to (3\mid m) and then (3\mid n). Step 3: Coprime numbers cannot have such a common factor.
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What is the correct answer to this question?
(m) and (n) both turn out divisible by (3)
Why is this the correct answer?
Step 1: From (\sqrt{3}=\frac{m}{n}), we get (m^2=3n^2). Step 2: This leads to (3\mid m) and then (3\mid n). Step 3: Coprime numbers cannot have such a common factor.
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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