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    Cube Root of −25

    Cube Root Calculator
    Cube root of

    What is the cube root of −25?

    Answer

    ∛(−25) =
    −∛25 ≈ −2.924

    Real cube root: the only number whose cube is −25.

    ≈ — rounded to 4 decimal places. −25 is not the cube of a rational number, so ∛(−25) is irrational: its decimal expansion never ends and never repeats.

    A negative number has a negative cube root: (−∛25)³ = −25. There is no real square root of −25.

    Sign
    ∛(−25) = −∛25, because (−a)³ = −a³
    Prime factors
    25 = 5 × 5 = 5²
    Take out of the root
    No prime appears three times, so ∛25 is already in simplest form.
    Between cubes
    2³ = 8 < 25 < 27 = 3³, so 2 < ∛25 < 3 and ∛25 ≈ 2.924

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    https://calculat.io/en/number/cube-root/-25Copy
    <a href="https://calculat.io/en/number/cube-root/-25">Cube Root of −25 (∛(−25)): Exact Value and Decimal</a>Copy
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    Cube Root of −25 (∛(−25)): Exact Value and Decimal. ∛(−25) = −∛25 ≈ −2.924. 25 has no cube factor but 1, so ∛25 is already simplest; it lies between 2 and 3. The minus comes out of the root.
    https://calculat.io/en/number/cube-root/-25/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    −49−∛49 ≈ −3.6593
    −32−2∛4 ≈ −3.1748
    −27−3
    −25−∛25 ≈ −2.924
    −21−∛21 ≈ −2.7589
    −20−∛20 ≈ −2.7144
    −15−∛15 ≈ −2.4662
    Recalculate with different values ↑

    FAQ

    What is the cube root of −25?

    ∛(−25) = −∛25 ≈ −2.924

    Why does the cube root of −25 exist but the square root does not?

    A cube keeps the sign: (−∛25)³ = −25, so ∛(−25) = −∛25. The square of any real number is never negative, so no real number squared gives −25.

    Is ∛(−25) a rational number?

    No: −25 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 ∛(−25) is irrational; its decimal never ends and never repeats: ∛(−25) ≈ −2.924.

    See Also