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    Cube Root of 243

    Cube Root Calculator
    Cube root of

    What is the cube root of 243?

    Answer

    ∛243 =
    3∛9 ≈ 6.2403

    Real cube root: the only number whose cube is 243.

    ≈ — rounded to 4 decimal places. 243 is not the cube of a rational number, so ∛243 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    243 = (3 × 3 × 3) × 3 × 3 = 3⁵
    Take out of the root
    ∛243 = ∛(3³ × 9) = 3∛9
    Between cubes
    6³ = 216 < 243 < 343 = 7³, so 6 < ∛243 < 7 and ∛243 ≈ 6.2403

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    https://calculat.io/en/number/cube-root/243Copy
    <a href="https://calculat.io/en/number/cube-root/243">Cube Root of 243 (∛243): Exact Value and Decimal</a>Copy
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    Cube Root of 243 (∛243): Exact Value and Decimal. ∛243 = 3∛9 ≈ 6.2403. 243 = 3³ × 9, so 3 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/243/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    239≈ 6.2058
    2402∛30 ≈ 6.2145
    242≈ 6.2317
    2433∛9 ≈ 6.2403
    245≈ 6.2573
    247≈ 6.2743
    2482∛31 ≈ 6.2828
    Recalculate with different values ↑

    FAQ

    What is the cube root of 243?

    ∛243 = 3∛9 ≈ 6.2403

    How to simplify ∛243?

    Factor 243 into primes: 243 = 3 × 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛243 = ∛(3³ × 9) = 3∛9.

    Is ∛243 a rational number?

    No: 243 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 ∛243 is irrational; its decimal never ends and never repeats: ∛243 ≈ 6.2403.

    See Also