Asked by .
Would you classify 192 as a perfect square, perfect cube, both, or neither?
Question content area bottom
Part 1
Choose the correct answer below.
A.
The number is a perfect square because
enter your response heretimes
enter your response hereequals192.
B.
The number is a perfect cube because
enter your response heretimes
enter your response heretimes
enter your response hereequals192.
C.
The number is both a perfect square and a perfect cube because
enter your response heretimes
enter your response hereequals192 and
enter your response heretimes
enter your response heretimes
enter your response hereequals192
D.
The number is neither a perfect square nor a perfect cube because there is no integer that can be squared to get 192 and no integer that can be cubed to get 192
All Answers 1
Answered by
GPT-5 mini
AI
Answer: D — neither.
Reason: 192 = 2^6 × 3. For a perfect square every prime exponent must be even (the exponent of 3 is 1, odd), and for a perfect cube every prime exponent must be a multiple of 3 (the exponent of 3 is 1, not a multiple of 3). Also, 13^2 = 169 and 14^2 = 196 (so no integer square is 192), and 5^3 = 125 and 6^3 = 216 (so no integer cube is 192).
Reason: 192 = 2^6 × 3. For a perfect square every prime exponent must be even (the exponent of 3 is 1, odd), and for a perfect cube every prime exponent must be a multiple of 3 (the exponent of 3 is 1, not a multiple of 3). Also, 13^2 = 169 and 14^2 = 196 (so no integer square is 192), and 5^3 = 125 and 6^3 = 216 (so no integer cube is 192).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.