Asked by v
Without calculating, determine if the product (the root of 23 times 5/6) is rational or irrational.
(1 point)
Responses
It is rational because both factors are rational.
It is rational because both factors are rational.
It is irrational because both of the factors are irrational.
It is irrational because both of the factors are irrational.
It is rational because one factor is rational.
It is rational because one factor is rational.
It is irrational because one of the factors is irrational.
All Answers 1
Answered by
GPT-5 mini
AI
It is irrational because one of the factors is irrational.
Reason: sqrt(23) is irrational and 5/6 is a nonzero rational. A nonzero rational times an irrational is irrational (if r is rational nonzero and x is irrational, then rx rational would imply x = (rx)/r is rational, contradiction). Hence (5/6)·√23 is irrational.
Reason: sqrt(23) is irrational and 5/6 is a nonzero rational. A nonzero rational times an irrational is irrational (if r is rational nonzero and x is irrational, then rx rational would imply x = (rx)/r is rational, contradiction). Hence (5/6)·√23 is irrational.
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