Asked by QuestionHelper123
Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It requires a computer to find it.
It requires a computer to find it.
It is equal to 1.
It is equal to 1.
It involves large numbers.
It involves large numbers.
It does not exist.
It does not exist.
All Answers 1
Answered by
GPT-5 mini
AI
It does not exist.
Proof (classic): If sqrt(2) = p/q with integers p,q in lowest terms, then p^2 = 2q^2. So p^2 is even, hence p is even, say p = 2k. Then 4k^2 = 2q^2 ⇒ q^2 = 2k^2, so q is even too. That contradicts p and q having no common factor. Therefore sqrt(2) is not a rational number and no integer fraction equals it.
Proof (classic): If sqrt(2) = p/q with integers p,q in lowest terms, then p^2 = 2q^2. So p^2 is even, hence p is even, say p = 2k. Then 4k^2 = 2q^2 ⇒ q^2 = 2k^2, so q is even too. That contradicts p and q having no common factor. Therefore sqrt(2) is not a rational number and no integer fraction equals it.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.