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    Cube Root of −2

    Cube Root Calculator
    Cube root of

    What is the cube root of −2?

    Answer

    ∛(−2) =
    −∛2 ≈ −1.2599

    Real cube root: the only number whose cube is −2.

    ≈ — rounded to 4 decimal places. −2 is not the cube of a rational number, so ∛(−2) is irrational: its decimal expansion never ends and never repeats.

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

    Sign
    ∛(−2) = −∛2, because (−a)³ = −a³
    Prime factors
    2 is a prime number: no triple of equal factors.
    Between cubes
    1³ = 1 < 2 < 8 = 2³, so 1 < ∛2 < 2 and ∛2 ≈ 1.2599

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    https://calculat.io/en/number/cube-root/-2Copy
    <a href="https://calculat.io/en/number/cube-root/-2">Cube Root of −2 (∛(−2)): Exact Value and Decimal</a>Copy
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    Cube Root of −2 (∛(−2)): Exact Value and Decimal. ∛(−2) = −∛2 ≈ −1.2599. 2 has no cube factor but 1, so ∛2 is already simplest; it lies between 1 and 2. The minus comes out of the root.
    https://calculat.io/en/number/cube-root/-2/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −7−∛7 ≈ −1.9129
    −5−∛5 ≈ −1.71
    −3−∛3 ≈ −1.4422
    −2−∛2 ≈ −1.2599
    −1−1
    −0.5≈ −0.7937
    −1/2−∛4/2 ≈ −0.7937
    Recalculate with different values ↑

    FAQ

    What is the cube root of −2?

    ∛(−2) = −∛2 ≈ −1.2599

    Why does the cube root of −2 exist but the square root does not?

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

    Is ∛(−2) a rational number?

    No: −2 is not the cube of a rational number, and the cube root of a fraction p/q in lowest terms is rational only when p and q are both cubes. So ∛(−2) is irrational; its decimal never ends and never repeats: ∛(−2) ≈ −1.2599.

    See Also