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    Cube Root of −1000

    Cube Root Calculator
    Cube root of

    What is the cube root of −1,000?

    Answer

    ∛(−1,000) =
    −10

    Real cube root: the only number whose cube is −1,000.

    A negative number has a negative cube root: (−10)³ = −1,000. There is no real square root of −1,000.

    Sign
    ∛(−1,000) = −∛1,000, because (−a)³ = −a³
    Prime factors
    1,000 = (2 × 2 × 2) × (5 × 5 × 5) = 2³ × 5³
    Take out of the root
    ∛1,000 = ∛(2³ × 5³) = 2 × 5 = 10
    Check
    10 × 10 × 10 = 1,000 ✓

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    https://calculat.io/en/number/cube-root/-1000Copy
    <a href="https://calculat.io/en/number/cube-root/-1000">Cube Root of −1000 (∛(−1000)): Exact Value and Decimal</a>Copy
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    Cube Root of −1000 (∛(−1000)): Exact Value and Decimal. ∛(−1,000) = −10. 1,000 = 10³: 10 × 10 × 10 = 1,000. The minus comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/-1000/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −2,197−13
    −1,728−12
    −1,331−11
    −1,000−10
    −729−9
    −512−8
    −343−7
    Recalculate with different values ↑

    FAQ

    What is the cube root of −1,000?

    ∛(−1,000) = −10

    Why does the cube root of −1,000 exist but the square root does not?

    A cube keeps the sign: (−10)³ = −1,000, so ∛(−1,000) = −10. The square of any real number is never negative, so no real number squared gives −1,000.

    Is ∛(−1,000) a rational number?

    Yes: ∛(−1,000) = −10, a whole number.

    See Also