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    Cube Root of 48

    Cube Root Calculator
    Cube root of

    What is the cube root of 48?

    Answer

    ∛48 =
    2∛6 ≈ 3.6342

    Real cube root: the only number whose cube is 48.

    ≈ — rounded to 4 decimal places. 48 is not the cube of a rational number, so ∛48 is irrational: its decimal expansion never ends and never repeats.

    Prime factors
    48 = (2 × 2 × 2) × 2 × 3 = 2⁴ × 3
    Take out of the root
    ∛48 = ∛(2³ × 6) = 2∛6
    Between cubes
    3³ = 27 < 48 < 64 = 4³, so 3 < ∛48 < 4 and ∛48 ≈ 3.6342

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    https://calculat.io/en/number/cube-root/48Copy
    <a href="https://calculat.io/en/number/cube-root/48">Cube Root of 48 (∛48): Exact Value and Decimal - Calculatio</a>Copy
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    Cube Root of 48 (∛48): Exact Value and Decimal. ∛48 = 2∛6 ≈ 3.6342. 48 = 2³ × 6, so 2 comes out of the root. Prime factors in threes and a check.
    https://calculat.io/en/number/cube-root/48/generated.jpgCopy

    Cube roots of nearby values

    N∛N
    45≈ 3.5569
    46≈ 3.583
    47≈ 3.6088
    482∛6 ≈ 3.6342
    49≈ 3.6593
    50≈ 3.684
    51≈ 3.7084
    Recalculate with different values ↑

    FAQ

    What is the cube root of 48?

    ∛48 = 2∛6 ≈ 3.6342

    How to simplify ∛48?

    Factor 48 into primes: 48 = 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: ∛48 = ∛(2³ × 6) = 2∛6.

    Is ∛48 a rational number?

    No: 48 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 ∛48 is irrational; its decimal never ends and never repeats: ∛48 ≈ 3.6342.

    See Also