Cube Root of 4/3

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What is the cube root of 4/3?

Answer

∛(4/3) =
∛36/3 ≈ 1.1006

Real cube root: the only number whose cube is 4/3.

≈ — rounded to 4 decimal places. 4/3 is not the cube of a rational number, so ∛(4/3) is irrational: its decimal expansion never ends and never repeats.

Root of a fraction
∛(4/3) = ∛4/∛3
Multiply by ∛(3²) = ∛9
∛4/∛3 = ∛36/∛27 = ∛36/3 ≈ 1.1006

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
5/4∛10/2 ≈ 1.0772
1.33≈ 1.0997
1.3311.1
4/3∛36/3 ≈ 1.1006
1.4≈ 1.1187
1.5≈ 1.1447
3/2∛12/2 ≈ 1.1447

FAQ

What is the cube root of 4/3?

∛(4/3) = ∛36/3 ≈ 1.1006

Why is ∛(4/3) = ∛36/3?

∛(4/3) = ∛4/∛3. Multiplying the numerator and the denominator by ∛(3²) = ∛9 makes the denominator a perfect cube: ∛36/∛27 = ∛36/3. The value does not change; only the root leaves the denominator.

Is ∛(4/3) a rational number?

No: 4/3 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 ∛(4/3) is irrational; its decimal never ends and never repeats: ∛(4/3) ≈ 1.1006.

See Also