What completes the proofs of (\sqrt{2}), (\sqrt{3}), and (\sqrt{5})?
Answer and explanation
Correct answer: Showing a common factor in numerator and denominator of a lowest-form fraction and writing contradiction
Step 1: All three proofs start with the rational assumption. Step 2: At the end, the same prime factor is found common in numerator and denominator. Step 3: This is impossible in a lowest-form fraction, so the proof is completed by contradiction.
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What is the correct answer to this question?
Showing a common factor in numerator and denominator of a lowest-form fraction and writing contradiction
Why is this the correct answer?
Step 1: All three proofs start with the rational assumption. Step 2: At the end, the same prime factor is found common in numerator and denominator. Step 3: This is impossible in a lowest-form fraction, so the proof is completed by contradiction.
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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