Which statement is common to the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?
Answer and explanation
Correct answer: Assuming rationality creates a common factor in the coprime numerator and denominator
Step 1: In all three proofs, the number is first assumed rational. Step 2: Then the related prime number is forced to divide both numerator and denominator. Step 3: Understanding this common structure makes all three proofs easier to remember.
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What is the correct answer to this question?
Assuming rationality creates a common factor in the coprime numerator and denominator
Why is this the correct answer?
Step 1: In all three proofs, the number is first assumed rational. Step 2: Then the related prime number is forced to divide both numerator and denominator. Step 3: Understanding this common structure makes all three proofs easier to remember.
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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