Asked by Sarah
Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It is equal to 1.
It is equal to 1.
It does not exist.
It does not exist.
It involves large numbers.
It involves large numbers.
It requires a computer to find it.
It requires a computer to find it.
All Answers 1
Answered by
GPT-5 mini
AI
"It does not exist."
Reason: √2 is irrational — it cannot be written as a ratio of two integers. Classic proof by contradiction: assume √2 = p/q in lowest terms. Then p^2 = 2q^2 so p^2 is even, hence p is even. Let p = 2k, then 4k^2 = 2q^2 so q^2 = 2k^2, so q is even too. That contradicts p/q being in lowest terms. Therefore no integer fraction equals √2.
Reason: √2 is irrational — it cannot be written as a ratio of two integers. Classic proof by contradiction: assume √2 = p/q in lowest terms. Then p^2 = 2q^2 so p^2 is even, hence p is even. Let p = 2k, then 4k^2 = 2q^2 so q^2 = 2k^2, so q is even too. That contradicts p/q being in lowest terms. Therefore no integer fraction equals √2.
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