Cube Root of 96

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Cube root of

What is the cube root of 96?

Answer

∛96 =
2∛12 ≈ 4.5789

Real cube root: the only number whose cube is 96.

≈ — rounded to 4 decimal places. 96 is not the cube of a rational number, so ∛96 is irrational: its decimal expansion never ends and never repeats.

Prime factors
96 = (2 × 2 × 2) × 2 × 2 × 3 = 2⁵ × 3
Take out of the root
∛96 = ∛(2³ × 12) = 2∛12
Between cubes
4³ = 64 < 96 < 125 = 5³, so 4 < ∛96 < 5 and ∛96 ≈ 4.5789

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
93≈ 4.5307
94≈ 4.5468
95≈ 4.5629
962∛12 ≈ 4.5789
97≈ 4.5947
98≈ 4.6104
99≈ 4.6261

FAQ

What is the cube root of 96?

∛96 = 2∛12 ≈ 4.5789

How to simplify ∛96?

Factor 96 into primes: 96 = 2 × 2 × 2 × 2 × 2 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛96 = ∛(2³ × 12) = 2∛12.

Is ∛96 a rational number?

No: 96 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 ∛96 is irrational; its decimal never ends and never repeats: ∛96 ≈ 4.5789.

See Also