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Which argument directly proves that (\sqrt{3}) cannot be rational?
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Answer and explanation
Correct answer: On assuming it rational, numerator and denominator both become divisible by (3)
Step 1: Taking (\sqrt{3}=\frac{p}{q}) gives (p^2=3q^2). Step 2: This forces both (p) and (q) to have (3) as a common factor. Step 3: That contradicts the condition of being coprime.
Frequently asked questions
What is the correct answer to this question?
On assuming it rational, numerator and denominator both become divisible by (3)
Why is this the correct answer?
Step 1: Taking (\sqrt{3}=\frac{p}{q}) gives (p^2=3q^2). Step 2: This forces both (p) and (q) to have (3) as a common factor. Step 3: That contradicts the condition of being coprime.
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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