Cube Root of −64

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Cube root of

What is the cube root of −64?

Answer

∛(−64) =
−4

Real cube root: the only number whose cube is −64.

A negative number has a negative cube root: (−4)³ = −64. There is no real square root of −64.

Sign
∛(−64) = −∛64, because (−a)³ = −a³
Prime factors
64 = (2 × 2 × 2) × (2 × 2 × 2) = 2⁶
Take out of the root
∛64 = ∛((2³)²) = 2² = 4
Check
4 × 4 × 4 = 64 ✓

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
−125−5
−108−3∛4 ≈ −4.7622
−81−3∛3 ≈ −4.3267
−64−4
−54−3∛2 ≈ −3.7798
−49−∛49 ≈ −3.6593
−32−2∛4 ≈ −3.1748

FAQ

What is the cube root of −64?

∛(−64) = −4

Why does the cube root of −64 exist but the square root does not?

A cube keeps the sign: (−4)³ = −64, so ∛(−64) = −4. The square of any real number is never negative, so no real number squared gives −64.

Is ∛(−64) a rational number?

Yes: ∛(−64) = −4, a whole number.

See Also