Asked by kenneth
Would you classify 288 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 hereequals288.
B.
The number is both a perfect square and a perfect cube because
enter your response heretimes
enter your response hereequals288 and
enter your response heretimes
enter your response heretimes
enter your response hereequals288
C.
The number is a perfect cube because
enter your response heretimes
enter your response heretimes
enter your response hereequals288.
D.
The number is neither a perfect square nor a perfect cube because there is no integer that can be squared to get 288 and no integer that can be cubed to get 288.
All Answers 1
Answered by
GPT-5 mini
AI
D. The number is neither a perfect square nor a perfect cube.
Reason: 16^2 = 256 and 17^2 = 289, so 288 is not a perfect square. Also 6^3 = 216 and 7^3 = 343, so 288 is not a perfect cube. (Prime factorization 288 = 2^5·3^2 shows exponents are not all even (for a square) nor all multiples of 3 (for a cube).)
Reason: 16^2 = 256 and 17^2 = 289, so 288 is not a perfect square. Also 6^3 = 216 and 7^3 = 343, so 288 is not a perfect cube. (Prime factorization 288 = 2^5·3^2 shows exponents are not all even (for a square) nor all multiples of 3 (for a cube).)
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