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    Cube Root of 1536

    Cube Root Calculator
    Cube root of

    What is the cube root of 1,536?

    Answer

    ∛1,536 =
    8∛3 ≈ 11.538

    Real cube root: the only number whose cube is 1,536.

    ≈ — rounded to 4 decimal places. 1,536 is not the cube of a rational number, so ∛1,536 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    1,536 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 3 = 2⁹ × 3
    Take out of the root
    ∛1,536 = ∛((2³)³ × 3) = 2³ × ∛3 = 8∛3
    Between cubes
    11³ = 1,331 < 1,536 < 1,728 = 12³, so 11 < ∛1,536 < 12 and ∛1,536 ≈ 11.538

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    https://calculat.io/en/number/cube-root/1536Copy
    <a href="https://calculat.io/en/number/cube-root/1536">Cube Root of 1536 (∛1536): Exact Value and Decimal</a>Copy
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    Cube Root of 1536 (∛1536): Exact Value and Decimal. ∛1,536 = 8∛3 ≈ 11.538. 1,536 = 8³ × 3, so 8 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/1536/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    1,4589∛2 ≈ 11.3393
    1,4882∛186 ≈ 11.4165
    1,521≈ 11.5003
    1,5368∛3 ≈ 11.538
    1,700≈ 11.9348
    1,7013∛63 ≈ 11.9372
    1,7157∛5 ≈ 11.9698
    Recalculate with different values ↑

    FAQ

    What is the cube root of 1,536?

    ∛1,536 = 8∛3 ≈ 11.538

    How to simplify ∛1,536?

    Factor 1,536 into primes: 1,536 = 2 × 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: ∛1,536 = ∛((2³)³ × 3) = 8∛3.

    Is ∛1,536 a rational number?

    No: 1,536 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 ∛1,536 is irrational; its decimal never ends and never repeats: ∛1,536 ≈ 11.538.

    See Also