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    Cube Root of −4096

    Cube Root Calculator
    Cube root of

    What is the cube root of −4,096?

    Answer

    ∛(−4,096) =
    −16

    Real cube root: the only number whose cube is −4,096.

    A negative number has a negative cube root: (−16)³ = −4,096. There is no real square root of −4,096.

    Sign
    ∛(−4,096) = −∛4,096, because (−a)³ = −a³
    Prime factors
    4,096 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = 2¹²
    Take out of the root
    ∛4,096 = ∛((2³)⁴) = 2⁴ = 16
    Check
    16 × 16 × 16 = 4,096 ✓

    See Also

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    https://calculat.io/en/number/cube-root/-4096Copy
    <a href="https://calculat.io/en/number/cube-root/-4096">Cube Root of −4096 (∛(−4096)): Exact Value and Decimal</a>Copy
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    Cube Root of −4096 (∛(−4096)): Exact Value and Decimal. ∛(−4,096) = −16. 4,096 = 16³: 16 × 16 × 16 = 4,096. The minus comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/-4096/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −6,859−19
    −5,832−18
    −4,913−17
    −4,096−16
    −3,375−15
    −2,744−14
    −2,197−13
    Recalculate with different values ↑

    FAQ

    What is the cube root of −4,096?

    ∛(−4,096) = −16

    Why does the cube root of −4,096 exist but the square root does not?

    A cube keeps the sign: (−16)³ = −4,096, so ∛(−4,096) = −16. The square of any real number is never negative, so no real number squared gives −4,096.

    Is ∛(−4,096) a rational number?

    Yes: ∛(−4,096) = −16, a whole number.

    See Also