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    Cube Root of 448

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    Cube root of

    What is the cube root of 448?

    Answer

    ∛448 =
    4∛7 ≈ 7.6517

    Real cube root: the only number whose cube is 448.

    ≈ — rounded to 4 decimal places. 448 is not the cube of a rational number, so ∛448 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    448 = (2 × 2 × 2) × (2 × 2 × 2) × 7 = 2⁶ × 7
    Take out of the root
    ∛448 = ∛((2³)² × 7) = 2² × ∛7 = 4∛7
    Between cubes
    7³ = 343 < 448 < 512 = 8³, so 7 < ∛448 < 8 and ∛448 ≈ 7.6517

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    https://calculat.io/en/number/cube-root/448Copy
    <a href="https://calculat.io/en/number/cube-root/448">Cube Root of 448 (∛448): Exact Value and Decimal</a>Copy
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    Cube Root of 448 (∛448): Exact Value and Decimal. ∛448 = 4∛7 ≈ 7.6517. 448 = 4³ × 7, so 4 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/448/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    425≈ 7.5185
    4326∛2 ≈ 7.5595
    445≈ 7.6346
    4484∛7 ≈ 7.6517
    450≈ 7.6631
    458≈ 7.7082
    474.5527.8
    Recalculate with different values ↑

    FAQ

    What is the cube root of 448?

    ∛448 = 4∛7 ≈ 7.6517

    How to simplify ∛448?

    Factor 448 into primes: 448 = 2 × 2 × 2 × 2 × 2 × 2 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛448 = ∛((2³)² × 7) = 4∛7.

    Is ∛448 a rational number?

    No: 448 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 ∛448 is irrational; its decimal never ends and never repeats: ∛448 ≈ 7.6517.

    See Also