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    Cube Root of 192

    Cube Root Calculator
    Cube root of

    What is the cube root of 192?

    Answer

    ∛192 =
    4∛3 ≈ 5.769

    Real cube root: the only number whose cube is 192.

    ≈ — rounded to 4 decimal places. 192 is not the cube of a rational number, so ∛192 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    192 = (2 × 2 × 2) × (2 × 2 × 2) × 3 = 2⁶ × 3
    Take out of the root
    ∛192 = ∛((2³)² × 3) = 2² × ∛3 = 4∛3
    Between cubes
    5³ = 125 < 192 < 216 = 6³, so 5 < ∛192 < 6 and ∛192 ≈ 5.769

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    https://calculat.io/en/number/cube-root/192Copy
    <a href="https://calculat.io/en/number/cube-root/192">Cube Root of 192 (∛192): Exact Value and Decimal</a>Copy
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    Cube Root of 192 (∛192): Exact Value and Decimal. ∛192 = 4∛3 ≈ 5.769. 192 = 4³ × 3, so 4 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/192/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    182≈ 5.6671
    187≈ 5.7185
    1893∛7 ≈ 5.7388
    1924∛3 ≈ 5.769
    196≈ 5.8088
    197≈ 5.8186
    2002∛25 ≈ 5.848
    Recalculate with different values ↑

    FAQ

    What is the cube root of 192?

    ∛192 = 4∛3 ≈ 5.769

    How to simplify ∛192?

    Factor 192 into primes: 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛192 = ∛((2³)² × 3) = 4∛3.

    Is ∛192 a rational number?

    No: 192 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 ∛192 is irrational; its decimal never ends and never repeats: ∛192 ≈ 5.769.

    See Also