Cube Root of 488

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Cube root of

What is the cube root of 488?

Answer

∛488 =
2∛61 ≈ 7.873

Real cube root: the only number whose cube is 488.

≈ — rounded to 4 decimal places. 488 is not the cube of a rational number, so ∛488 is irrational: its decimal expansion never ends and never repeats.

Prime factors
488 = (2 × 2 × 2) × 61 = 2³ × 61
Take out of the root
∛488 = ∛(2³ × 61) = 2∛61
Between cubes
7³ = 343 < 488 < 512 = 8³, so 7 < ∛488 < 8 and ∛488 ≈ 7.873

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
458≈ 7.7082
474.5527.8
4802∛60 ≈ 7.8297
4882∛61 ≈ 7.873
490≈ 7.8837
5005∛4 ≈ 7.937
5128

FAQ

What is the cube root of 488?

∛488 = 2∛61 ≈ 7.873

How to simplify ∛488?

Factor 488 into primes: 488 = 2 × 2 × 2 × 61. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛488 = ∛(2³ × 61) = 2∛61.

Is ∛488 a rational number?

No: 488 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 ∛488 is irrational; its decimal never ends and never repeats: ∛488 ≈ 7.873.

See Also