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    Cube Root of 768

    Cube Root Calculator
    Cube root of

    What is the cube root of 768?

    Answer

    ∛768 =
    4∛12 ≈ 9.1577

    Real cube root: the only number whose cube is 768.

    ≈ — rounded to 4 decimal places. 768 is not the cube of a rational number, so ∛768 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    768 = (2 × 2 × 2) × (2 × 2 × 2) × 2 × 2 × 3 = 2⁸ × 3
    Take out of the root
    ∛768 = ∛((2³)² × 12) = 2² × ∛12 = 4∛12
    Between cubes
    9³ = 729 < 768 < 1,000 = 10³, so 9 < ∛768 < 10 and ∛768 ≈ 9.1577

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    https://calculat.io/en/number/cube-root/768Copy
    <a href="https://calculat.io/en/number/cube-root/768">Cube Root of 768 (∛768): Exact Value and Decimal</a>Copy
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    Cube Root of 768 (∛768): Exact Value and Decimal. ∛768 = 4∛12 ≈ 9.1577. 768 = 4³ × 12, so 4 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/768/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    700≈ 8.879
    7299
    730≈ 9.0041
    7684∛12 ≈ 9.1577
    8646∛4 ≈ 9.5244
    900≈ 9.6549
    925≈ 9.7435
    Recalculate with different values ↑

    FAQ

    What is the cube root of 768?

    ∛768 = 4∛12 ≈ 9.1577

    How to simplify ∛768?

    Factor 768 into primes: 768 = 2 × 2 × 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: ∛768 = ∛((2³)² × 12) = 4∛12.

    Is ∛768 a rational number?

    No: 768 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 ∛768 is irrational; its decimal never ends and never repeats: ∛768 ≈ 9.1577.

    See Also