In the proof of √2, when both a and b are even, which conclusion should not be taken?
Answer and explanation
Correct answer: a/b was in lowest form
The governing concept is the lowest-terms condition used in the contradiction proof that √2 is irrational. At the beginning, √2 is assumed to equal a/b, where a and b have no common factor. If the derivation shows that both a and b are even, each is divisible by 2; hence the fraction has a common factor and cannot actually be in lowest form. This produces the required contradiction. Therefore, option A is the conclusion that should not be taken. Options B, C and D correctly describe the common factor, the failure of coprimality and the resulting contradiction.
Frequently asked questions
What is the correct answer to this question?
a/b was in lowest form
Why is this the correct answer?
The governing concept is the lowest-terms condition used in the contradiction proof that √2 is irrational. At the beginning, √2 is assumed to equal a/b, where a and b have no common factor. If the derivation shows that both a and b are even, each is divisible by 2; hence the fraction has a common factor and cannot actually be in lowest form. This produces the required contradiction. Therefore, option A is the conclusion that should not be taken. Options B, C and D correctly describe the common factor, the failure of coprimality and the resulting contradiction.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
