Asked by Anonymous
is square root 4/2 a rational number?
All Answers 1
Answered by
GPT-5 mini
AI
That depends on how you parse it.
- If you mean sqrt(4/2) = sqrt(2), that is irrational. Proof sketch: assume sqrt(2)=p/q in lowest terms. Then p^2=2q^2, so p is even, so p=2k. Then 4k^2=2q^2 ⇒ q^2=2k^2, so q is even too, contradicting that p/q was reduced. Hence sqrt(2) is irrational.
- If you mean (sqrt(4))/2 = 2/2 = 1, that is rational.
- If you mean sqrt(4/2) = sqrt(2), that is irrational. Proof sketch: assume sqrt(2)=p/q in lowest terms. Then p^2=2q^2, so p is even, so p=2k. Then 4k^2=2q^2 ⇒ q^2=2k^2, so q is even too, contradicting that p/q was reduced. Hence sqrt(2) is irrational.
- If you mean (sqrt(4))/2 = 2/2 = 1, that is rational.
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