Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Cube Root of −21

    Cube Root Calculator
    Cube root of

    What is the cube root of −21?

    Answer

    ∛(−21) =
    −∛21 ≈ −2.7589

    Real cube root: the only number whose cube is −21.

    ≈ — rounded to 4 decimal places. −21 is not the cube of a rational number, so ∛(−21) is irrational: its decimal expansion never ends and never repeats.

    A negative number has a negative cube root: (−∛21)³ = −21. There is no real square root of −21.

    Sign
    ∛(−21) = −∛21, because (−a)³ = −a³
    Prime factors
    21 = 3 × 7
    Take out of the root
    No prime appears three times, so ∛21 is already in simplest form.
    Between cubes
    2³ = 8 < 21 < 27 = 3³, so 2 < ∛21 < 3 and ∛21 ≈ 2.7589

    Related Calculations

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/cube-root/-21Copy
    <a href="https://calculat.io/en/number/cube-root/-21">Cube Root of −21 (∛(−21)): Exact Value and Decimal</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Cube Root of −21 (∛(−21)): Exact Value and Decimal. ∛(−21) = −∛21 ≈ −2.7589. 21 has no cube factor but 1, so ∛21 is already simplest; it lies between 2 and 3. The minus comes out of the root.
    https://calculat.io/en/number/cube-root/-21/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −32−2∛4 ≈ −3.1748
    −27−3
    −25−∛25 ≈ −2.924
    −21−∛21 ≈ −2.7589
    −20−∛20 ≈ −2.7144
    −15−∛15 ≈ −2.4662
    −8−2
    Recalculate with different values ↑

    FAQ

    What is the cube root of −21?

    ∛(−21) = −∛21 ≈ −2.7589

    Why does the cube root of −21 exist but the square root does not?

    A cube keeps the sign: (−∛21)³ = −21, so ∛(−21) = −∛21. The square of any real number is never negative, so no real number squared gives −21.

    Is ∛(−21) a rational number?

    No: −21 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 ∛(−21) is irrational; its decimal never ends and never repeats: ∛(−21) ≈ −2.7589.

    See Also