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    Cube Root of 3125

    Cube Root Calculator
    Cube root of

    What is the cube root of 3,125?

    Answer

    ∛3,125 =
    5∛25 ≈ 14.6201

    Real cube root: the only number whose cube is 3,125.

    ≈ — rounded to 4 decimal places. 3,125 is not the cube of a rational number, so ∛3,125 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    3,125 = (5 × 5 × 5) × 5 × 5 = 5⁵
    Take out of the root
    ∛3,125 = ∛(5³ × 25) = 5∛25
    Between cubes
    14³ = 2,744 < 3,125 < 3,375 = 15³, so 14 < ∛3,125 < 15 and ∛3,125 ≈ 14.6201

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    https://calculat.io/en/number/cube-root/3125Copy
    <a href="https://calculat.io/en/number/cube-root/3125">Cube Root of 3125 (∛3125): Exact Value and Decimal</a>Copy
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    Cube Root of 3125 (∛3125): Exact Value and Decimal. ∛3,125 = 5∛25 ≈ 14.6201. 3,125 = 5³ × 25, so 5 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/3125/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    2,8804∛45 ≈ 14.2276
    2,917≈ 14.2882
    3,0877∛9 ≈ 14.5606
    3,1255∛25 ≈ 14.6201
    3,1364∛49 ≈ 14.6372
    3,37515
    3,8886∛18 ≈ 15.7244
    Recalculate with different values ↑

    FAQ

    What is the cube root of 3,125?

    ∛3,125 = 5∛25 ≈ 14.6201

    How to simplify ∛3,125?

    Factor 3,125 into primes: 3,125 = 5 × 5 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛3,125 = ∛(5³ × 25) = 5∛25.

    Is ∛3,125 a rational number?

    No: 3,125 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 ∛3,125 is irrational; its decimal never ends and never repeats: ∛3,125 ≈ 14.6201.

    See Also