Cube Root of 1/4

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What is the cube root of 1/4?

Answer

∛(1/4) =
∛2/2 ≈ 0.63

Real cube root: the only number whose cube is 1/4.

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

1/4 = 0.25.

Root of a fraction
∛(1/4) = ∛1/∛4 = 1/∛4
Multiply by ∛(4²) = ∛16
1/∛4 = ∛16/∛64 = ∛16/4
Take out of the root
∛16/4 = ∛(2³ × 2)/4 = 2∛2/4 = ∛2/2 ≈ 0.63

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2/9∛6/3 ≈ 0.6057
125/5125/8 = 0.625
0.25≈ 0.63
1/4∛2/2 ≈ 0.63
8/272/3 ≈ 0.6667
0.3≈ 0.6694
1/3∛9/3 ≈ 0.6934

FAQ

What is the cube root of 1/4?

∛(1/4) = ∛2/2 ≈ 0.63

Why is ∛(1/4) = ∛2/2?

∛(1/4) = ∛1/∛4. Multiplying the numerator and the denominator by ∛(4²) = ∛16 makes the denominator a perfect cube: ∛16/∛64 = ∛16/4. Taking the cubes out of ∛16 and reducing gives ∛2/2. The value does not change; only the root leaves the denominator.

Is ∛(1/4) a rational number?

No: 1/4 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 ∛(1/4) is irrational; its decimal never ends and never repeats: ∛(1/4) ≈ 0.63.

See Also