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    Cube Root of −8

    Cube Root Calculator
    Cube root of

    What is the cube root of −8?

    Answer

    ∛(−8) =
    −2

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

    A negative number has a negative cube root: (−2)³ = −8. There is no real square root of −8.

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

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    https://calculat.io/en/number/cube-root/-8Copy
    <a href="https://calculat.io/en/number/cube-root/-8">Cube Root of −8 (∛(−8)): Exact Value and Decimal</a>Copy
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    Cube Root of −8 (∛(−8)): Exact Value and Decimal. ∛(−8) = −2. 8 = 2³: 2 × 2 × 2 = 8. The minus comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/-8/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −21−∛21 ≈ −2.7589
    −20−∛20 ≈ −2.7144
    −15−∛15 ≈ −2.4662
    −8−2
    −7−∛7 ≈ −1.9129
    −5−∛5 ≈ −1.71
    −3−∛3 ≈ −1.4422
    Recalculate with different values ↑

    FAQ

    What is the cube root of −8?

    ∛(−8) = −2

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

    A cube keeps the sign: (−2)³ = −8, so ∛(−8) = −2. The square of any real number is never negative, so no real number squared gives −8.

    Is ∛(−8) a rational number?

    Yes: ∛(−8) = −2, a whole number.

    See Also