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    Cube Root of 200

    Cube Root Calculator
    Cube root of

    What is the cube root of 200?

    Answer

    ∛200 =
    2∛25 ≈ 5.848

    Real cube root: the only number whose cube is 200.

    ≈ — rounded to 4 decimal places. 200 is not the cube of a rational number, so ∛200 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    200 = (2 × 2 × 2) × 5 × 5 = 2³ × 5²
    Take out of the root
    ∛200 = ∛(2³ × 25) = 2∛25
    Between cubes
    5³ = 125 < 200 < 216 = 6³, so 5 < ∛200 < 6 and ∛200 ≈ 5.848

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    https://calculat.io/en/number/cube-root/200Copy
    <a href="https://calculat.io/en/number/cube-root/200">Cube Root of 200 (∛200): Exact Value and Decimal</a>Copy
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    Cube Root of 200 (∛200): Exact Value and Decimal. ∛200 = 2∛25 ≈ 5.848. 200 = 2³ × 25, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/200/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    1924∛3 ≈ 5.769
    196≈ 5.8088
    197≈ 5.8186
    2002∛25 ≈ 5.848
    201≈ 5.8578
    207≈ 5.9155
    2082∛26 ≈ 5.925
    Recalculate with different values ↑

    FAQ

    What is the cube root of 200?

    ∛200 = 2∛25 ≈ 5.848

    How to simplify ∛200?

    Factor 200 into primes: 200 = 2 × 2 × 2 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛200 = ∛(2³ × 25) = 2∛25.

    Is ∛200 a rational number?

    No: 200 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 ∛200 is irrational; its decimal never ends and never repeats: ∛200 ≈ 5.848.

    See Also