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    Cube Root of −1/2

    Cube Root Calculator
    Cube root of

    What is the cube root of −1/2?

    Answer

    ∛(−1/2) =
    −∛4/2 ≈ −0.7937

    Real cube root: the only number whose cube is −1/2.

    ≈ — rounded to 4 decimal places. −1/2 is not the cube of a rational number, so ∛(−1/2) is irrational: its decimal expansion never ends and never repeats.

    A negative number has a negative cube root: (−∛4/2)³ = −1/2. There is no real square root of −1/2.

    −1/2 = −0.5.

    Sign
    ∛(−1/2) = −∛(1/2), because (−a)³ = −a³
    Root of a fraction
    ∛(1/2) = ∛1/∛2 = 1/∛2
    Multiply by ∛(2²) = ∛4
    1/∛2 = ∛4/∛8 = ∛4/2 ≈ 0.7937

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    https://calculat.io/en/number/cube-root/-1-2Copy
    <a href="https://calculat.io/en/number/cube-root/-1-2">Cube Root of −1/2 (∛(−1/2)): Exact Value and Decimal</a>Copy
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    Cube Root of −1/2 (∛(−1/2)): Exact Value and Decimal. ∛(−1/2) = −∛4/2 ≈ −0.7937. ∛(1/2) = ∛1/∛2; multiplying by ∛4 clears the root from the denominator. The minus comes out of the root.
    https://calculat.io/en/number/cube-root/-1-2/generated.jpgCopy

    FAQ

    What is the cube root of −1/2?

    ∛(−1/2) = −∛4/2 ≈ −0.7937

    Why does the cube root of −1/2 exist but the square root does not?

    A cube keeps the sign: (−∛4/2)³ = −1/2, so ∛(−1/2) = −∛4/2. The square of any real number is never negative, so no real number squared gives −1/2.

    Is ∛(−1/2) a rational number?

    No: −1/2 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 ∛(−1/2) is irrational; its decimal never ends and never repeats: ∛(−1/2) ≈ −0.7937.