- A64
- B16
- C36
- D216
Step-by-Step Solution
64 = and , so it is both. 16 and 36 are squares but not cubes; is a cube but not a square. To be both, every prime exponent must be a multiple of 6, and the smallest such number above 1 is .
Answer: A) 64
What is the smallest number greater than 1 that is both a perfect square and a perfect cube?
Class 8Cubes and Cube RootsCubes and Roots
Key idea: Squares vs cubes — what's different
Both are repeated multiplication, but with key differences:
- A square is non-negative: .
- A cube **keeps the sign**: . (Three negatives stay odd → still negative.)
- Squares grow more slowly than cubes: vs For square roots, only positive results (by convention). For cube roots, the sign matches the input: ∛.
- A square is non-negative: .
- A cube **keeps the sign**: . (Three negatives stay odd → still negative.)
- Squares grow more slowly than cubes: vs For square roots, only positive results (by convention). For cube roots, the sign matches the input: ∛.
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