which numbers are perfect cubes? check all that apply.

3
64
81
125
999
3,000

Question

which numbers are perfect cubes? check all that apply.

3
  64
  81
  125
  999
  3,000

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Perfect Cubes" ], "current_concepts": [ "Perfect Cubes" ] } ## Define perfect cubes A perfect cube is an integer that can be written as the cube of another integer: $$ n = k^3 \quad \text{for } k \in \mathbb{Z} $$ ## Test each given number Evaluate each option to see if it has an integer cube root: $$ \begin{aligned} &\sqrt[3]{3} \approx 1.44 \quad (\text{Not an integer})\ &\sqrt[3]{64} = 4 \quad (4^3 = 64)\ &\sqrt[3]{81} \approx 4.33 \quad (\text{Not an integer})\ &\sqrt[3]{125} = 5 \quad (5^3 = 125)\ &\sqrt[3]{999} \approx 10.00 \quad (\text{Not an integer})\ &\sqrt[3]{3000} \approx 14.42 \quad (\text{Not an integer}) \end{aligned} $$ ## Identify the correct options The numbers that are perfect cubes are $64$ and $125$.

3

64

81

125

999

3,000

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Perfect Cubes" ] }

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QUESTION IMAGE

Question

Explanation:

Define perfect cubes

Test each given number

Identify the correct options

Answer: