Cube Root of 1/3

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Cube root of

What is the cube root of 1/3?

Answer

∛(1/3) =
∛9/3 ≈ 0.6934

Real cube root: the only number whose cube is 1/3.

≈ — rounded to 4 decimal places. 1/3 is not the cube of a rational number, so ∛(1/3) is irrational: its decimal expansion never ends and never repeats.

Root of a fraction
∛(1/3) = ∛1/∛3 = 1/∛3
Multiply by ∛(3²) = ∛9
1/∛3 = ∛9/∛27 = ∛9/3 ≈ 0.6934

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1/4∛2/2 ≈ 0.63
8/272/3 ≈ 0.6667
0.3≈ 0.6694
1/3∛9/3 ≈ 0.6934
0.3430.7
343/10007/10 = 0.7
0.36≈ 0.7114

FAQ

What is the cube root of 1/3?

∛(1/3) = ∛9/3 ≈ 0.6934

Why is ∛(1/3) = ∛9/3?

∛(1/3) = ∛1/∛3. Multiplying the numerator and the denominator by ∛(3²) = ∛9 makes the denominator a perfect cube: ∛9/∛27 = ∛9/3. The value does not change; only the root leaves the denominator.

Is ∛(1/3) a rational number?

No: 1/3 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 ∛(1/3) is irrational; its decimal never ends and never repeats: ∛(1/3) ≈ 0.6934.

See Also