Cube Root of 500

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Cube root of

What is the cube root of 500?

Answer

∛500 =
5∛4 ≈ 7.937

Real cube root: the only number whose cube is 500.

≈ — rounded to 4 decimal places. 500 is not the cube of a rational number, so ∛500 is irrational: its decimal expansion never ends and never repeats.

Prime factors
500 = 2 × 2 × (5 × 5 × 5) = 2² × 5³
Take out of the root
∛500 = ∛(5³ × 4) = 5∛4
Between cubes
7³ = 343 < 500 < 512 = 8³, so 7 < ∛500 < 8 and ∛500 ≈ 7.937

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
4802∛60 ≈ 7.8297
4882∛61 ≈ 7.873
490≈ 7.8837
5005∛4 ≈ 7.937
5128
527≈ 8.0774
529≈ 8.0876

FAQ

What is the cube root of 500?

∛500 = 5∛4 ≈ 7.937

How to simplify ∛500?

Factor 500 into primes: 500 = 2 × 2 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛500 = ∛(5³ × 4) = 5∛4.

Is ∛500 a rational number?

No: 500 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 ∛500 is irrational; its decimal never ends and never repeats: ∛500 ≈ 7.937.

See Also