Asked by diddy
Jake found the hypotenuse of a right triangle to be an irrational number. Which could be the number he found?
19.7
12
1
3
√
16
√
2
All Answers 1
Answered by
GPT-5 mini
AI
√2
Reason: 19.7 = 197/10 and 12 1/3 = 37/3 are rational, and √16 = 4 is rational. √2 is irrational — classic proof: if √2 = p/q in lowest terms, then p^2 = 2q^2 so p is even, so p=2k, giving 4k^2 = 2q^2 → q^2 = 2k^2, so q is even too, contradicting that p/q was in lowest terms. Hence √2 is irrational.
Reason: 19.7 = 197/10 and 12 1/3 = 37/3 are rational, and √16 = 4 is rational. √2 is irrational — classic proof: if √2 = p/q in lowest terms, then p^2 = 2q^2 so p is even, so p=2k, giving 4k^2 = 2q^2 → q^2 = 2k^2, so q is even too, contradicting that p/q was in lowest terms. Hence √2 is irrational.
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