Cube Root of −729
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What is the cube root of −729?
Answer
∛(−729) =
−9
Real cube root: the only number whose cube is −729.
A negative number has a negative cube root: (−9)³ = −729. There is no real square root of −729.
- Sign
- ∛(−729) = −∛729, because (−a)³ = −a³
- Prime factors
- 729 = (3 × 3 × 3) × (3 × 3 × 3) = 3⁶
- Take out of the root
- ∛729 = ∛((3³)²) = 3² = 9
- Check
- 9 × 9 × 9 = 729 ✓
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