Cube Root of 12800

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What is the cube root of 12,800?

Answer

∛12,800 =
8∛25 ≈ 23.3921

Real cube root: the only number whose cube is 12,800.

≈ — rounded to 4 decimal places. 12,800 is not the cube of a rational number, so ∛12,800 is irrational: its decimal expansion never ends and never repeats.

Prime factors
12,800 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 5 × 5 = 2⁹ × 5²
Take out of the root
∛12,800 = ∛((2³)³ × 25) = 2³ × ∛25 = 8∛25
Between cubes
23³ = 12,167 < 12,800 < 13,824 = 24³, so 23 < ∛12,800 < 24 and ∛12,800 ≈ 23.3921

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
10,64822
11,025≈ 22.2566
12,16723
12,8008∛25 ≈ 23.3921
13,82424
15,62525
17,57626

FAQ

What is the cube root of 12,800?

∛12,800 = 8∛25 ≈ 23.3921

How to simplify ∛12,800?

Factor 12,800 into primes: 12,800 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛12,800 = ∛((2³)³ × 25) = 8∛25.

Is ∛12,800 a rational number?

No: 12,800 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 ∛12,800 is irrational; its decimal never ends and never repeats: ∛12,800 ≈ 23.3921.

See Also