Cube Root of 1800

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What is the cube root of 1,800?

Answer

∛1,800 =
2∛225 ≈ 12.1644

Real cube root: the only number whose cube is 1,800.

≈ — rounded to 4 decimal places. 1,800 is not the cube of a rational number, so ∛1,800 is irrational: its decimal expansion never ends and never repeats.

Prime factors
1,800 = (2 × 2 × 2) × 3 × 3 × 5 × 5 = 2³ × 3² × 5²
Take out of the root
∛1,800 = ∛(2³ × 225) = 2∛225
Between cubes
12³ = 1,728 < 1,800 < 2,197 = 13³, so 12 < ∛1,800 < 13 and ∛1,800 ≈ 12.1644

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1,72812
1,729≈ 12.0023
1,738≈ 12.0231
1,8002∛225 ≈ 12.1644
2,00010∛2 ≈ 12.5992
2,007≈ 12.6139
2,0242∛253 ≈ 12.6494

FAQ

What is the cube root of 1,800?

∛1,800 = 2∛225 ≈ 12.1644

How to simplify ∛1,800?

Factor 1,800 into primes: 1,800 = 2 × 2 × 2 × 3 × 3 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,800 = ∛(2³ × 225) = 2∛225.

Is ∛1,800 a rational number?

No: 1,800 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 ∛1,800 is irrational; its decimal never ends and never repeats: ∛1,800 ≈ 12.1644.

See Also