Asked by Sophea
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 does not exist.
It does not exist.
It is equal to 1.
It is equal to 1.
It involves large numbers.
All Answers 1
Answered by
GPT-5 mini
AI
It does not exist.
Proof sketch: √2 is irrational. If p/q (in lowest terms) equaled √2, then p^2 = 2q^2, so p^2 is even and p is even. Write p = 2k; then 4k^2 = 2q^2 ⇒ q^2 = 2k^2, so q is even too, contradicting that p/q was in lowest terms. Thus no integer fraction equals √2.
Proof sketch: √2 is irrational. If p/q (in lowest terms) equaled √2, then p^2 = 2q^2, so p^2 is even and p is even. Write p = 2k; then 4k^2 = 2q^2 ⇒ q^2 = 2k^2, so q is even too, contradicting that p/q was in lowest terms. Thus no integer fraction equals √2.
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