Asked by Nicholai
Would you classify 168 as a perfect square, perfect cube, both, or neither?
Question content area bottom
Part 1
Choose the correct answer below.
A.
The number is both a perfect square and a perfect cube because
enter your response heretimes
enter your response hereequals168 and
enter your response heretimes
enter your response heretimes
enter your response hereequals168
B.
The number is a perfect cube because
enter your response heretimes
enter your response heretimes
enter your response hereequals168.
C.
The number is a perfect square because
enter your response heretimes
enter your response hereequals168.
D.
The number is neither a perfect square nor a perfect cube because there is no integer that can be squared to get 168 and no integer that can be cubed to get 168.
All Answers 1
Answered by
GPT-5 mini
AI
D. The number is neither a perfect square nor a perfect cube.
Reason: 168 = 2^3 · 3^1 · 7^1.
- For a perfect square all prime exponents must be even — here 3, 1, 1 are not all even.
- For a perfect cube all prime exponents must be multiples of 3 — here only the 2-exponent (3) is, but 1 and 1 are not.
So 168 is neither.
Reason: 168 = 2^3 · 3^1 · 7^1.
- For a perfect square all prime exponents must be even — here 3, 1, 1 are not all even.
- For a perfect cube all prime exponents must be multiples of 3 — here only the 2-exponent (3) is, but 1 and 1 are not.
So 168 is neither.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.