Cube Root of 480

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Cube root of

What is the cube root of 480?

Answer

∛480 =
2∛60 ≈ 7.8297

Real cube root: the only number whose cube is 480.

≈ — rounded to 4 decimal places. 480 is not the cube of a rational number, so ∛480 is irrational: its decimal expansion never ends and never repeats.

Prime factors
480 = (2 × 2 × 2) × 2 × 2 × 3 × 5 = 2⁵ × 3 × 5
Take out of the root
∛480 = ∛(2³ × 60) = 2∛60
Between cubes
7³ = 343 < 480 < 512 = 8³, so 7 < ∛480 < 8 and ∛480 ≈ 7.8297

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
450≈ 7.6631
458≈ 7.7082
474.5527.8
4802∛60 ≈ 7.8297
4882∛61 ≈ 7.873
490≈ 7.8837
5005∛4 ≈ 7.937

FAQ

What is the cube root of 480?

∛480 = 2∛60 ≈ 7.8297

How to simplify ∛480?

Factor 480 into primes: 480 = 2 × 2 × 2 × 2 × 2 × 3 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛480 = ∛(2³ × 60) = 2∛60.

Is ∛480 a rational number?

No: 480 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 ∛480 is irrational; its decimal never ends and never repeats: ∛480 ≈ 7.8297.

See Also