Cube Root of −512
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What is the cube root of −512?
Answer
∛(−512) =
−8
Real cube root: the only number whose cube is −512.
A negative number has a negative cube root: (−8)³ = −512. There is no real square root of −512.
- Sign
- ∛(−512) = −∛512, because (−a)³ = −a³
- Prime factors
- 512 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 2⁹
- Take out of the root
- ∛512 = ∛((2³)³) = 2³ = 8
- Check
- 8 × 8 × 8 = 512 ✓
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