Cube Root of 108

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What is the cube root of 108?

Answer

∛108 =
3∛4 ≈ 4.7622

Real cube root: the only number whose cube is 108.

≈ — rounded to 4 decimal places. 108 is not the cube of a rational number, so ∛108 is irrational: its decimal expansion never ends and never repeats.

Prime factors
108 = 2 × 2 × (3 × 3 × 3) = 2² × 3³
Take out of the root
∛108 = ∛(3³ × 4) = 3∛4
Between cubes
4³ = 64 < 108 < 125 = 5³, so 4 < ∛108 < 5 and ∛108 ≈ 4.7622

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Recalculate with different values ↑

Cube roots of nearby values

N∛N
102≈ 4.6723
103≈ 4.6875
107≈ 4.7475
1083∛4 ≈ 4.7622
110≈ 4.7914
110.5924.8
111≈ 4.8059

FAQ

What is the cube root of 108?

∛108 = 3∛4 ≈ 4.7622

How to simplify ∛108?

Factor 108 into primes: 108 = 2 × 2 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛108 = ∛(3³ × 4) = 3∛4.

Is ∛108 a rational number?

No: 108 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 ∛108 is irrational; its decimal never ends and never repeats: ∛108 ≈ 4.7622.

See Also