Cube Root of 280

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Cube root of

What is the cube root of 280?

Answer

∛280 =
2∛35 ≈ 6.5421

Real cube root: the only number whose cube is 280.

≈ — rounded to 4 decimal places. 280 is not the cube of a rational number, so ∛280 is irrational: its decimal expansion never ends and never repeats.

Prime factors
280 = (2 × 2 × 2) × 5 × 7 = 2³ × 5 × 7
Take out of the root
∛280 = ∛(2³ × 35) = 2∛35
Between cubes
6³ = 216 < 280 < 343 = 7³, so 6 < ∛280 < 7 and ∛280 ≈ 6.5421

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
258≈ 6.3661
276≈ 6.5108
279≈ 6.5343
2802∛35 ≈ 6.5421
285≈ 6.5808
2882∛36 ≈ 6.6039
289≈ 6.6115

FAQ

What is the cube root of 280?

∛280 = 2∛35 ≈ 6.5421

How to simplify ∛280?

Factor 280 into primes: 280 = 2 × 2 × 2 × 5 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛280 = ∛(2³ × 35) = 2∛35.

Is ∛280 a rational number?

No: 280 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 ∛280 is irrational; its decimal never ends and never repeats: ∛280 ≈ 6.5421.

See Also