Cube Root of 8788

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What is the cube root of 8,788?

Answer

∛8,788 =
13∛4 ≈ 20.6362

Real cube root: the only number whose cube is 8,788.

≈ — rounded to 4 decimal places. 8,788 is not the cube of a rational number, so ∛8,788 is irrational: its decimal expansion never ends and never repeats.

Prime factors
8,788 = 2 × 2 × (13 × 13 × 13) = 2² × 13³
Take out of the root
∛8,788 = ∛(13³ × 4) = 13∛4
Between cubes
20³ = 8,000 < 8,788 < 9,261 = 21³, so 20 < ∛8,788 < 21 and ∛8,788 ≈ 20.6362

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
7,2909∛10 ≈ 19.3899
7,7766∛36 ≈ 19.8116
8,00020
8,78813∛4 ≈ 20.6362
9,26121
9,621≈ 21.2687
9,999≈ 21.5436

FAQ

What is the cube root of 8,788?

∛8,788 = 13∛4 ≈ 20.6362

How to simplify ∛8,788?

Factor 8,788 into primes: 8,788 = 2 × 2 × 13 × 13 × 13. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛8,788 = ∛(13³ × 4) = 13∛4.

Is ∛8,788 a rational number?

No: 8,788 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 ∛8,788 is irrational; its decimal never ends and never repeats: ∛8,788 ≈ 20.6362.

See Also