Choose the correct order in the proof of √2.
Answer and explanation
Correct answer: Rational assumption → a² = 2b² → a even → b even → contradiction
The correct answer is A because it follows the contradiction proof in the required logical order. Assume √2 is rational and write it as a/b in lowest terms, where a and b are coprime integers and b is nonzero. Squaring gives a²/b² = 2, hence a² = 2b². Therefore a² is even, so a is even; write a = 2k. Substitution gives 4k² = 2b², or b² = 2k², so b is also even. Thus both a and b have a common factor 2, contradicting the assumption that the fraction was in lowest terms. The other sequences omit the essential algebra or replace proof with an unsupported decimal guess.
Frequently asked questions
What is the correct answer to this question?
Rational assumption → a² = 2b² → a even → b even → contradiction
Why is this the correct answer?
The correct answer is A because it follows the contradiction proof in the required logical order. Assume √2 is rational and write it as a/b in lowest terms, where a and b are coprime integers and b is nonzero. Squaring gives a²/b² = 2, hence a² = 2b². Therefore a² is even, so a is even; write a = 2k. Substitution gives 4k² = 2b², or b² = 2k², so b is also even. Thus both a and b have a common factor 2, contradicting the assumption that the fraction was in lowest terms. The other sequences omit the essential algebra or replace proof with an unsupported decimal guess.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.
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