Cube Root of −216
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What is the cube root of −216?
Answer
∛(−216) =
−6
Real cube root: the only number whose cube is −216.
A negative number has a negative cube root: (−6)³ = −216. There is no real square root of −216.
- Sign
- ∛(−216) = −∛216, because (−a)³ = −a³
- Prime factors
- 216 = (2 × 2 × 2) × (3 × 3 × 3) = 2³ × 3³
- Take out of the root
- ∛216 = ∛(2³ × 3³) = 2 × 3 = 6
- Check
- 6 × 6 × 6 = 216 ✓
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