Which option explains why the rational assumption for (\sqrt{3}) breaks?
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Answer and explanation
Correct answer: Because both numerator and denominator of the lowest-form fraction are found divisible by (3)
Step 1: Assuming rationality, (\sqrt{3}=\frac{p}{q}) is written in lowest form. Step 2: The proof shows both (p) and (q) divisible by (3). Step 3: Such a common factor cannot occur in a lowest-form fraction.
Frequently asked questions
What is the correct answer to this question?
Because both numerator and denominator of the lowest-form fraction are found divisible by (3)
Why is this the correct answer?
Step 1: Assuming rationality, (\sqrt{3}=\frac{p}{q}) is written in lowest form. Step 2: The proof shows both (p) and (q) divisible by (3). Step 3: Such a common factor cannot occur in a lowest-form fraction.
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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