Cube Root of 458

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Cube root of

What is the cube root of 458?

Answer

∛458 ≈
7.7082

Real cube root: the only number whose cube is 458.

≈ — rounded to 4 decimal places. 458 is not the cube of a rational number, so ∛458 is irrational: its decimal expansion never ends and never repeats.

Prime factors
458 = 2 × 229
Take out of the root
No prime appears three times, so ∛458 is already in simplest form.
Between cubes
7³ = 343 < 458 < 512 = 8³, so 7 < ∛458 < 8 and ∛458 ≈ 7.7082

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
445≈ 7.6346
4484∛7 ≈ 7.6517
450≈ 7.6631
458≈ 7.7082
474.5527.8
4802∛60 ≈ 7.8297
4882∛61 ≈ 7.873

FAQ

What is the cube root of 458?

∛458 ≈ 7.7082

Can ∛458 be simplified?

No: no prime appears three times in 458, so its only cube factor is 1 and ∛458 is already in simplest form. Since 7³ = 343 < 458 < 512 = 8³, ∛458 lies between 7 and 8: ∛458 ≈ 7.7082.

Is ∛458 a rational number?

No: 458 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 ∛458 is irrational; its decimal never ends and never repeats: ∛458 ≈ 7.7082.

See Also