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    Cube Root of 1200

    Cube Root Calculator
    Cube root of

    What is the cube root of 1,200?

    Answer

    ∛1,200 =
    2∛150 ≈ 10.6266

    Real cube root: the only number whose cube is 1,200.

    ≈ — rounded to 4 decimal places. 1,200 is not the cube of a rational number, so ∛1,200 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    1,200 = (2 × 2 × 2) × 2 × 3 × 5 × 5 = 2⁴ × 3 × 5²
    Take out of the root
    ∛1,200 = ∛(2³ × 150) = 2∛150
    Between cubes
    10³ = 1,000 < 1,200 < 1,331 = 11³, so 10 < ∛1,200 < 11 and ∛1,200 ≈ 10.6266

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    https://calculat.io/en/number/cube-root/1200Copy
    <a href="https://calculat.io/en/number/cube-root/1200">Cube Root of 1200 (∛1200): Exact Value and Decimal</a>Copy
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    Cube Root of 1200 (∛1200): Exact Value and Decimal. ∛1,200 = 2∛150 ≈ 10.6266. 1,200 = 2³ × 150, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/1200/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    1,0806∛5 ≈ 10.2599
    1,089≈ 10.2883
    1,1255∛9 ≈ 10.4004
    1,2002∛150 ≈ 10.6266
    1,210≈ 10.656
    1,225≈ 10.6999
    1,2804∛20 ≈ 10.8577
    Recalculate with different values ↑

    FAQ

    What is the cube root of 1,200?

    ∛1,200 = 2∛150 ≈ 10.6266

    How to simplify ∛1,200?

    Factor 1,200 into primes: 1,200 = 2 × 2 × 2 × 2 × 3 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,200 = ∛(2³ × 150) = 2∛150.

    Is ∛1,200 a rational number?

    No: 1,200 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 ∛1,200 is irrational; its decimal never ends and never repeats: ∛1,200 ≈ 10.6266.

    See Also