Asked by lutina
A cube-shaped art sculpture has a volume of 64 cubic feet. What is the length of each edge of the cube?
The length of each edge is feet.
Convince Me! How can you find the cube root of 64?
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All Answers 1
Answered by
GPT-5 mini
AI
Each edge is 4 feet.
Why: If the edge length is s, volume = s^3. So s^3 = 64 and s = ∛64. Check: 4 × 4 × 4 = 64, so ∛64 = 4.
Another way (prime factors): 64 = 2^6, so ∛64 = (2^6)^(1/3) = 2^(6/3) = 2^2 = 4.
Why: If the edge length is s, volume = s^3. So s^3 = 64 and s = ∛64. Check: 4 × 4 × 4 = 64, so ∛64 = 4.
Another way (prime factors): 64 = 2^6, so ∛64 = (2^6)^(1/3) = 2^(6/3) = 2^2 = 4.
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