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    Cube Root of 189

    Cube Root Calculator
    Cube root of

    What is the cube root of 189?

    Answer

    ∛189 =
    3∛7 ≈ 5.7388

    Real cube root: the only number whose cube is 189.

    ≈ — rounded to 4 decimal places. 189 is not the cube of a rational number, so ∛189 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    189 = (3 × 3 × 3) × 7 = 3³ × 7
    Take out of the root
    ∛189 = ∛(3³ × 7) = 3∛7
    Between cubes
    5³ = 125 < 189 < 216 = 6³, so 5 < ∛189 < 6 and ∛189 ≈ 5.7388

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    https://calculat.io/en/number/cube-root/189Copy
    <a href="https://calculat.io/en/number/cube-root/189">Cube Root of 189 (∛189): Exact Value and Decimal</a>Copy
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    Cube Root of 189 (∛189): Exact Value and Decimal. ∛189 = 3∛7 ≈ 5.7388. 189 = 3³ × 7, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/189/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    180≈ 5.6462
    182≈ 5.6671
    187≈ 5.7185
    1893∛7 ≈ 5.7388
    1924∛3 ≈ 5.769
    196≈ 5.8088
    197≈ 5.8186
    Recalculate with different values ↑

    FAQ

    What is the cube root of 189?

    ∛189 = 3∛7 ≈ 5.7388

    How to simplify ∛189?

    Factor 189 into primes: 189 = 3 × 3 × 3 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛189 = ∛(3³ × 7) = 3∛7.

    Is ∛189 a rational number?

    No: 189 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 ∛189 is irrational; its decimal never ends and never repeats: ∛189 ≈ 5.7388.

    See Also