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What is the cube root of 1,280?

Answer

∛1,280 =
4∛20 ≈ 10.8577

Real cube root: the only number whose cube is 1,280.

≈ — rounded to 4 decimal places. 1,280 is not the cube of a rational number, so ∛1,280 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,280 = (2 × 2 × 2) × (2 × 2 × 2) × 2 × 2 × 5 = 2⁸ × 5
Take out of the root
∛1,280 = ∛((2³)² × 20) = 2² × ∛20 = 4∛20
Between cubes
10³ = 1,000 < 1,280 < 1,331 = 11³, so 10 < ∛1,280 < 11 and ∛1,280 ≈ 10.8577

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,2002∛150 ≈ 10.6266
1,210≈ 10.656
1,225≈ 10.6999
1,2804∛20 ≈ 10.8577
1,2966∛6 ≈ 10.9027
1,3233∛49 ≈ 10.9779
1,33111

FAQ

What is the cube root of 1,280?

∛1,280 = 4∛20 ≈ 10.8577

How to simplify ∛1,280?

Factor 1,280 into primes: 1,280 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,280 = ∛((2³)² × 20) = 4∛20.

Is ∛1,280 a rational number?

No: 1,280 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 ∛1,280 is irrational; its decimal never ends and never repeats: ∛1,280 ≈ 10.8577.

See Also