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    Cube Root of 1323

    Cube Root Calculator
    Cube root of

    What is the cube root of 1,323?

    Answer

    ∛1,323 =
    3∛49 ≈ 10.9779

    Real cube root: the only number whose cube is 1,323.

    ≈ — rounded to 4 decimal places. 1,323 is not the cube of a rational number, so ∛1,323 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    1,323 = (3 × 3 × 3) × 7 × 7 = 3³ × 7²
    Take out of the root
    ∛1,323 = ∛(3³ × 49) = 3∛49
    Between cubes
    10³ = 1,000 < 1,323 < 1,331 = 11³, so 10 < ∛1,323 < 11 and ∛1,323 ≈ 10.9779

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    https://calculat.io/en/number/cube-root/1323Copy
    <a href="https://calculat.io/en/number/cube-root/1323">Cube Root of 1323 (∛1323): Exact Value and Decimal</a>Copy
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    Cube Root of 1323 (∛1323): Exact Value and Decimal. ∛1,323 = 3∛49 ≈ 10.9779. 1,323 = 3³ × 49, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/1323/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    1,225≈ 10.6999
    1,2804∛20 ≈ 10.8577
    1,2966∛6 ≈ 10.9027
    1,3233∛49 ≈ 10.9779
    1,33111
    1,332≈ 11.0028
    1,369≈ 11.1037
    Recalculate with different values ↑

    FAQ

    What is the cube root of 1,323?

    ∛1,323 = 3∛49 ≈ 10.9779

    How to simplify ∛1,323?

    Factor 1,323 into primes: 1,323 = 3 × 3 × 3 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,323 = ∛(3³ × 49) = 3∛49.

    Is ∛1,323 a rational number?

    No: 1,323 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 ∛1,323 is irrational; its decimal never ends and never repeats: ∛1,323 ≈ 10.9779.

    See Also