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    Cube Root of −7

    Cube Root Calculator
    Cube root of

    What is the cube root of −7?

    Answer

    ∛(−7) =
    −∛7 ≈ −1.9129

    Real cube root: the only number whose cube is −7.

    ≈ — rounded to 4 decimal places. −7 is not the cube of a rational number, so ∛(−7) is irrational: its decimal expansion never ends and never repeats.

    A negative number has a negative cube root: (−∛7)³ = −7. There is no real square root of −7.

    Sign
    ∛(−7) = −∛7, because (−a)³ = −a³
    Prime factors
    7 is a prime number: no triple of equal factors.
    Between cubes
    1³ = 1 < 7 < 8 = 2³, so 1 < ∛7 < 2 and ∛7 ≈ 1.9129

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    https://calculat.io/en/number/cube-root/-7Copy
    <a href="https://calculat.io/en/number/cube-root/-7">Cube Root of −7 (∛(−7)): Exact Value and Decimal</a>Copy
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    Cube Root of −7 (∛(−7)): Exact Value and Decimal. ∛(−7) = −∛7 ≈ −1.9129. 7 has no cube factor but 1, so ∛7 is already simplest; it lies between 1 and 2. The minus comes out of the root.
    https://calculat.io/en/number/cube-root/-7/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −20−∛20 ≈ −2.7144
    −15−∛15 ≈ −2.4662
    −8−2
    −7−∛7 ≈ −1.9129
    −5−∛5 ≈ −1.71
    −3−∛3 ≈ −1.4422
    −2−∛2 ≈ −1.2599
    Recalculate with different values ↑

    FAQ

    What is the cube root of −7?

    ∛(−7) = −∛7 ≈ −1.9129

    Why does the cube root of −7 exist but the square root does not?

    A cube keeps the sign: (−∛7)³ = −7, so ∛(−7) = −∛7. The square of any real number is never negative, so no real number squared gives −7.

    Is ∛(−7) a rational number?

    No: −7 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 ∛(−7) is irrational; its decimal never ends and never repeats: ∛(−7) ≈ −1.9129.

    See Also