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    Cube Root of 2401

    Cube Root Calculator
    Cube root of

    What is the cube root of 2,401?

    Answer

    ∛2,401 =
    7∛7 ≈ 13.3905

    Real cube root: the only number whose cube is 2,401.

    ≈ — rounded to 4 decimal places. 2,401 is not the cube of a rational number, so ∛2,401 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    2,401 = (7 × 7 × 7) × 7 = 7⁴
    Take out of the root
    ∛2,401 = ∛(7³ × 7) = 7∛7
    Between cubes
    13³ = 2,197 < 2,401 < 2,744 = 14³, so 13 < ∛2,401 < 14 and ∛2,401 ≈ 13.3905

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    https://calculat.io/en/number/cube-root/2401Copy
    <a href="https://calculat.io/en/number/cube-root/2401">Cube Root of 2401 (∛2401): Exact Value and Decimal</a>Copy
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    Cube Root of 2401 (∛2401): Exact Value and Decimal. ∛2,401 = 7∛7 ≈ 13.3905. 2,401 = 7³ × 7, so 7 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/2401/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    2,2002∛275 ≈ 13.0059
    2,300≈ 13.2001
    2,4002∛300 ≈ 13.3887
    2,4017∛7 ≈ 13.3905
    2,450≈ 13.481
    2,5926∛12 ≈ 13.7366
    2,74414
    Recalculate with different values ↑

    FAQ

    What is the cube root of 2,401?

    ∛2,401 = 7∛7 ≈ 13.3905

    How to simplify ∛2,401?

    Factor 2,401 into primes: 2,401 = 7 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,401 = ∛(7³ × 7) = 7∛7.

    Is ∛2,401 a rational number?

    No: 2,401 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 ∛2,401 is irrational; its decimal never ends and never repeats: ∛2,401 ≈ 13.3905.

    See Also