Cube Root of 1/2

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Cube root of

What is the cube root of 1/2?

Answer

∛(1/2) =
∛4/2 ≈ 0.7937

Real cube root: the only number whose cube is 1/2.

≈ — rounded to 4 decimal places. 1/2 is not the cube of a rational number, so ∛(1/2) is irrational: its decimal expansion never ends and never repeats.

1/2 = 0.5.

Root of a fraction
∛(1/2) = ∛1/∛2 = 1/∛2
Multiply by ∛(2²) = ∛4
1/∛2 = ∛4/∛8 = ∛4/2 ≈ 0.7937

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
27/643/4 = 0.75
343/7297/9 ≈ 0.7778
0.5≈ 0.7937
1/2∛4/2 ≈ 0.7937
0.5120.8
64/1254/5 = 0.8
125/2165/6 ≈ 0.8333

FAQ

What is the cube root of 1/2?

∛(1/2) = ∛4/2 ≈ 0.7937

Why is ∛(1/2) = ∛4/2?

∛(1/2) = ∛1/∛2. Multiplying the numerator and the denominator by ∛(2²) = ∛4 makes the denominator a perfect cube: ∛4/∛8 = ∛4/2. The value does not change; only the root leaves the denominator.

Is ∛(1/2) a rational number?

No: 1/2 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 ∛(1/2) is irrational; its decimal never ends and never repeats: ∛(1/2) ≈ 0.7937.

See Also