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    Cube Root of −8000

    Cube Root Calculator
    Cube root of

    What is the cube root of −8,000?

    Answer

    ∛(−8,000) =
    −20

    Real cube root: the only number whose cube is −8,000.

    A negative number has a negative cube root: (−20)³ = −8,000. There is no real square root of −8,000.

    Sign
    ∛(−8,000) = −∛8,000, because (−a)³ = −a³
    Prime factors
    8,000 = (2 × 2 × 2) × (2 × 2 × 2) × (5 × 5 × 5) = 2⁶ × 5³
    Take out of the root
    ∛8,000 = ∛((2³)² × 5³) = 2² × 5 = 20
    Check
    20 × 20 × 20 = 8,000 ✓

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    https://calculat.io/en/number/cube-root/-8000Copy
    <a href="https://calculat.io/en/number/cube-root/-8000">Cube Root of −8000 (∛(−8000)): Exact Value and Decimal</a>Copy
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    Cube Root of −8000 (∛(−8000)): Exact Value and Decimal. ∛(−8,000) = −20. 8,000 = 20³: 20 × 20 × 20 = 8,000. The minus comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/-8000/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −106,875−5∛855 ≈ −47.4561
    −8,000−20
    −6,859−19
    −5,832−18
    −4,913−17
    −4,096−16
    −3,375−15
    Recalculate with different values ↑

    FAQ

    What is the cube root of −8,000?

    ∛(−8,000) = −20

    Why does the cube root of −8,000 exist but the square root does not?

    A cube keeps the sign: (−20)³ = −8,000, so ∛(−8,000) = −20. The square of any real number is never negative, so no real number squared gives −8,000.

    Is ∛(−8,000) a rational number?

    Yes: ∛(−8,000) = −20, a whole number.

    See Also