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    Cube Root of −20

    Cube Root Calculator
    Cube root of

    What is the cube root of −20?

    Answer

    ∛(−20) =
    −∛20 ≈ −2.7144

    Real cube root: the only number whose cube is −20.

    ≈ — rounded to 4 decimal places. −20 is not the cube of a rational number, so ∛(−20) is irrational: its decimal expansion never ends and never repeats.

    A negative number has a negative cube root: (−∛20)³ = −20. There is no real square root of −20.

    Sign
    ∛(−20) = −∛20, because (−a)³ = −a³
    Prime factors
    20 = 2 × 2 × 5 = 2² × 5
    Take out of the root
    No prime appears three times, so ∛20 is already in simplest form.
    Between cubes
    2³ = 8 < 20 < 27 = 3³, so 2 < ∛20 < 3 and ∛20 ≈ 2.7144

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    https://calculat.io/en/number/cube-root/-20Copy
    <a href="https://calculat.io/en/number/cube-root/-20">Cube Root of −20 (∛(−20)): Exact Value and Decimal</a>Copy
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    Cube Root of −20 (∛(−20)): Exact Value and Decimal. ∛(−20) = −∛20 ≈ −2.7144. 20 has no cube factor but 1, so ∛20 is already simplest; it lies between 2 and 3. The minus comes out of the root.
    https://calculat.io/en/number/cube-root/-20/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −27−3
    −25−∛25 ≈ −2.924
    −21−∛21 ≈ −2.7589
    −20−∛20 ≈ −2.7144
    −15−∛15 ≈ −2.4662
    −8−2
    −7−∛7 ≈ −1.9129
    Recalculate with different values ↑

    FAQ

    What is the cube root of −20?

    ∛(−20) = −∛20 ≈ −2.7144

    Why does the cube root of −20 exist but the square root does not?

    A cube keeps the sign: (−∛20)³ = −20, so ∛(−20) = −∛20. The square of any real number is never negative, so no real number squared gives −20.

    Is ∛(−20) a rational number?

    No: −20 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 ∛(−20) is irrational; its decimal never ends and never repeats: ∛(−20) ≈ −2.7144.

    See Also