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    Cube Root of −106875

    Cube Root Calculator
    Cube root of

    What is the cube root of −106,875?

    Answer

    ∛(−106,875) =
    −5∛855 ≈ −47.4561

    Real cube root: the only number whose cube is −106,875.

    ≈ — rounded to 4 decimal places. −106,875 is not the cube of a rational number, so ∛(−106,875) is irrational: its decimal expansion never ends and never repeats.

    A negative number has a negative cube root: (−5∛855)³ = −106,875. There is no real square root of −106,875.

    Sign
    ∛(−106,875) = −∛106,875, because (−a)³ = −a³
    Prime factors
    106,875 = 3 × 3 × (5 × 5 × 5) × 5 × 19 = 3² × 5⁴ × 19
    Take out of the root
    ∛106,875 = ∛(5³ × 855) = 5∛855
    Between cubes
    47³ = 103,823 < 106,875 < 110,592 = 48³, so 47 < ∛106,875 < 48 and ∛106,875 ≈ 47.4561

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    <a href="https://calculat.io/en/number/cube-root/-106875">Cube Root of −106875 (∛(−106875)): Exact Value and Decimal</a>Copy
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    Cube Root of −106875 (∛(−106875)): Exact Value and Decimal. ∛(−106,875) = −5∛855 ≈ −47.4561. 106,875 = 5³ × 855, so 5 comes out of the root. The minus comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/-106875/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −106,875−5∛855 ≈ −47.4561
    −8,000−20
    −6,859−19
    −5,832−18
    −4,913−17
    −4,096−16
    −3,375−15
    Recalculate with different values ↑

    FAQ

    What is the cube root of −106,875?

    ∛(−106,875) = −5∛855 ≈ −47.4561

    Why does the cube root of −106,875 exist but the square root does not?

    A cube keeps the sign: (−5∛855)³ = −106,875, so ∛(−106,875) = −5∛855. The square of any real number is never negative, so no real number squared gives −106,875.

    Is ∛(−106,875) a rational number?

    No: −106,875 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 ∛(−106,875) is irrational; its decimal never ends and never repeats: ∛(−106,875) ≈ −47.4561.

    See Also