Cube Root of 4/5

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What is the cube root of 4/5?

Answer

∛(4/5) =
∛100/5 ≈ 0.9283

Real cube root: the only number whose cube is 4/5.

≈ — rounded to 4 decimal places. 4/5 is not the cube of a rational number, so ∛(4/5) is irrational: its decimal expansion never ends and never repeats.

4/5 = 0.8.

Root of a fraction
∛(4/5) = ∛4/∛5
Multiply by ∛(5²) = ∛25
∛4/∛5 = ∛100/∛125 = ∛100/5 ≈ 0.9283

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
729/10009/10 = 0.9
3/4∛6/2 ≈ 0.9086
0.8≈ 0.9283
4/5∛100/5 ≈ 0.9283
11
1.1≈ 1.0323
1.12≈ 1.0385

FAQ

What is the cube root of 4/5?

∛(4/5) = ∛100/5 ≈ 0.9283

Why is ∛(4/5) = ∛100/5?

∛(4/5) = ∛4/∛5. Multiplying the numerator and the denominator by ∛(5²) = ∛25 makes the denominator a perfect cube: ∛100/∛125 = ∛100/5. The value does not change; only the root leaves the denominator.

Is ∛(4/5) a rational number?

No: 4/5 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 ∛(4/5) is irrational; its decimal never ends and never repeats: ∛(4/5) ≈ 0.9283.

See Also