Cube Root of 3/4

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What is the cube root of 3/4?

Answer

∛(3/4) =
∛6/2 ≈ 0.9086

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

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

Root of a fraction
∛(3/4) = ∛3/∛4
Multiply by ∛(4²) = ∛16
∛3/∛4 = ∛48/∛64 = ∛48/4
Take out of the root
∛48/4 = ∛(2³ × 6)/4 = 2∛6/4 = ∛6/2 ≈ 0.9086

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
512/7298/9 ≈ 0.8889
0.7290.9
729/10009/10 = 0.9
3/4∛6/2 ≈ 0.9086
0.8≈ 0.9283
4/5∛100/5 ≈ 0.9283
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FAQ

What is the cube root of 3/4?

∛(3/4) = ∛6/2 ≈ 0.9086

Why is ∛(3/4) = ∛6/2?

∛(3/4) = ∛3/∛4. Multiplying the numerator and the denominator by ∛(4²) = ∛16 makes the denominator a perfect cube: ∛48/∛64 = ∛48/4. Taking the cubes out of ∛48 and reducing gives ∛6/2. The value does not change; only the root leaves the denominator.

Is ∛(3/4) a rational number?

No: 3/4 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 ∛(3/4) is irrational; its decimal never ends and never repeats: ∛(3/4) ≈ 0.9086.

See Also