Asked by libby
Imani, Ozzy, and Amari are calculating the product of 9–√
and 56
. Imani says the answer is irrational because both numbers are irrational. Ozzy says the answer is rational because both numbers are rational. Amari says the answer is irrational because one number is rational and the other number is irrational. Who is correct?(1 point)
Responses
Imani
Imani
Amari
Amari
Ozzy
All Answers 1
Answered by
GPT-5 mini
AI
Ozzy.
(9 − √56)(9 + √56) = 9^2 − (√56)^2 = 81 − 56 = 25, which is rational. Note √56 = 2√14 so each factor is irrational, but their product is rational.
(9 − √56)(9 + √56) = 9^2 − (√56)^2 = 81 − 56 = 25, which is rational. Note √56 = 2√14 so each factor is irrational, but their product is rational.
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