Cube Root of 120

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Cube root of

What is the cube root of 120?

Answer

∛120 =
2∛15 ≈ 4.9324

Real cube root: the only number whose cube is 120.

≈ — rounded to 4 decimal places. 120 is not the cube of a rational number, so ∛120 is irrational: its decimal expansion never ends and never repeats.

Prime factors
120 = (2 × 2 × 2) × 3 × 5 = 2³ × 3 × 5
Take out of the root
∛120 = ∛(2³ × 15) = 2∛15
Between cubes
4³ = 64 < 120 < 125 = 5³, so 4 < ∛120 < 5 and ∛120 ≈ 4.9324

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
115≈ 4.8629
117≈ 4.891
119≈ 4.9187
1202∛15 ≈ 4.9324
121≈ 4.9461
122≈ 4.9597
123≈ 4.9732

FAQ

What is the cube root of 120?

∛120 = 2∛15 ≈ 4.9324

How to simplify ∛120?

Factor 120 into primes: 120 = 2 × 2 × 2 × 3 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛120 = ∛(2³ × 15) = 2∛15.

Is ∛120 a rational number?

No: 120 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 ∛120 is irrational; its decimal never ends and never repeats: ∛120 ≈ 4.9324.

See Also