Why is it necessary to take (\frac{p}{q}) in lowest form while proving the irrationality of (\sqrt{2})?
Answer and explanation
Correct answer: So that getting a common factor at the end becomes a contradiction
Step 1: A rational number is written in lowest form as (\frac{p}{q}). Step 2: The proof shows that both (p) and (q) become even, which contradicts lowest form. Step 3: Always mention coprime at the start of the proof.
Frequently asked questions
What is the correct answer to this question?
So that getting a common factor at the end becomes a contradiction
Why is this the correct answer?
Step 1: A rational number is written in lowest form as (\frac{p}{q}). Step 2: The proof shows that both (p) and (q) become even, which contradicts lowest form. Step 3: Always mention coprime at the start of the proof.
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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