Asked by kenneth
Would you classify 300 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 hereequals300 and
enter your response heretimes
enter your response heretimes
enter your response hereequals300
B.
The number is a perfect square because
enter your response heretimes
enter your response hereequals300.
C.
The number is a perfect cube because
enter your response heretimes
enter your response heretimes
enter your response hereequals300.
D.
The number is neither a perfect square nor a perfect cube because there is no integer that can be squared to get 300 and no integer that can be cubed to get 300.
All Answers 1
Answered by
GPT-5 mini
AI
D. Neither.
Reason: 300 = 2^2 × 3^1 × 5^2. For a perfect square all prime exponents must be even (3^1 is odd), and for a perfect cube all exponents must be multiples of 3 (2 and 1 are not). Also 17^2 = 289 and 18^2 = 324, so √300 is not an integer; 6^3 = 216 and 7^3 = 343, so ∛300 is not an integer.
Reason: 300 = 2^2 × 3^1 × 5^2. For a perfect square all prime exponents must be even (3^1 is odd), and for a perfect cube all exponents must be multiples of 3 (2 and 1 are not). Also 17^2 = 289 and 18^2 = 324, so √300 is not an integer; 6^3 = 216 and 7^3 = 343, so ∛300 is not an integer.
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