Cube Root of 2/9

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What is the cube root of 2/9?

Answer

∛(2/9) =
∛6/3 ≈ 0.6057

Real cube root: the only number whose cube is 2/9.

≈ — rounded to 4 decimal places. 2/9 is not the cube of a rational number, so ∛(2/9) is irrational: its decimal expansion never ends and never repeats.

Root of a fraction
∛(2/9) = ∛2/∛9
Multiply by ∛(9²) = ∛81
∛2/∛9 = ∛162/∛729 = ∛162/9
Take out of the root
∛162/9 = ∛(3³ × 6)/9 = 3∛6/9 = ∛6/3 ≈ 0.6057

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
0.2≈ 0.5848
0.2160.6
27/1253/5 = 0.6
2/9∛6/3 ≈ 0.6057
125/5125/8 = 0.625
0.25≈ 0.63
1/4∛2/2 ≈ 0.63

FAQ

What is the cube root of 2/9?

∛(2/9) = ∛6/3 ≈ 0.6057

Why is ∛(2/9) = ∛6/3?

∛(2/9) = ∛2/∛9. Multiplying the numerator and the denominator by ∛(9²) = ∛81 makes the denominator a perfect cube: ∛162/∛729 = ∛162/9. Taking the cubes out of ∛162 and reducing gives ∛6/3. The value does not change; only the root leaves the denominator.

Is ∛(2/9) a rational number?

No: 2/9 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 ∛(2/9) is irrational; its decimal never ends and never repeats: ∛(2/9) ≈ 0.6057.

See Also