Cube Root of 2200

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What is the cube root of 2,200?

Answer

∛2,200 =
2∛275 ≈ 13.0059

Real cube root: the only number whose cube is 2,200.

≈ — rounded to 4 decimal places. 2,200 is not the cube of a rational number, so ∛2,200 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,200 = (2 × 2 × 2) × 5 × 5 × 11 = 2³ × 5² × 11
Take out of the root
∛2,200 = ∛(2³ × 275) = 2∛275
Between cubes
13³ = 2,197 < 2,200 < 2,744 = 14³, so 13 < ∛2,200 < 14 and ∛2,200 ≈ 13.0059

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2,007≈ 12.6139
2,0242∛253 ≈ 12.6494
2,19713
2,2002∛275 ≈ 13.0059
2,300≈ 13.2001
2,4002∛300 ≈ 13.3887
2,4017∛7 ≈ 13.3905

FAQ

What is the cube root of 2,200?

∛2,200 = 2∛275 ≈ 13.0059

How to simplify ∛2,200?

Factor 2,200 into primes: 2,200 = 2 × 2 × 2 × 5 × 5 × 11. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛2,200 = ∛(2³ × 275) = 2∛275.

Is ∛2,200 a rational number?

No: 2,200 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 ∛2,200 is irrational; its decimal never ends and never repeats: ∛2,200 ≈ 13.0059.

See Also