- A6
- B8
- C22
- D7
Step-by-Step Solution
is under 500 while goes over, so 7 is the largest. Answering 22 uses the square root of 500 (about 22.4) instead of the cube root, and 6 stops one step early at 216.
Answer: D) 7
Rani needs the largest whole number whose cube is still less than 500. Which number is it?
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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