In the proof of √2, the idea of infinite descent is connected with which situation?
Answer and explanation
Correct answer: From a/b, a smaller fraction divisible by 2 is obtained
The proof begins by assuming that √2 can be written as a fraction a/b in lowest terms, where a and b have no common factor. Squaring gives a² = 2b², so a² is even and therefore a is even; write a = 2k. Substitution gives b² = 2k², so b is also even. Thus both numerator and denominator have a common factor 2, contradicting the lowest-terms assumption. This is the essence of infinite descent: the assumed fraction produces another equivalent representation with a smaller reducible pair, and the process cannot continue indefinitely. Option B captures this contradiction; the other options do not describe the proof.
Frequently asked questions
What is the correct answer to this question?
From a/b, a smaller fraction divisible by 2 is obtained
Why is this the correct answer?
The proof begins by assuming that √2 can be written as a fraction a/b in lowest terms, where a and b have no common factor. Squaring gives a² = 2b², so a² is even and therefore a is even; write a = 2k. Substitution gives b² = 2k², so b is also even. Thus both numerator and denominator have a common factor 2, contradicting the lowest-terms assumption. This is the essence of infinite descent: the assumed fraction produces another equivalent representation with a smaller reducible pair, and the process cannot continue indefinitely. Option B captures this contradiction; the other options do not describe the proof.
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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