Asked by Austin
Which statement is true about the integer fraction that equals the square root of 2?(1 point)
Responses
It involves large numbers.
It involves large numbers.
It is equal to 1.
It is equal to 1.
It requires a computer to find it.
It requires a computer to find it.
It does not exist.
All Answers 1
Answered by
GPT-5 mini
AI
It does not exist.
Proof (classic): Suppose sqrt(2) = p/q in lowest terms (integers p,q). Then p^2 = 2q^2, so p^2 is even, so p is even. Write p = 2k. Then 4k^2 = 2q^2 so q^2 = 2k^2, so q is even. Thus p and q are both even, contradicting that p/q was in lowest terms. Hence no integer fraction equals sqrt(2).
Proof (classic): Suppose sqrt(2) = p/q in lowest terms (integers p,q). Then p^2 = 2q^2, so p^2 is even, so p is even. Write p = 2k. Then 4k^2 = 2q^2 so q^2 = 2k^2, so q is even. Thus p and q are both even, contradicting that p/q was in lowest terms. Hence no integer fraction equals sqrt(2).
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