Cube Root of 5/3

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What is the cube root of 5/3?

Answer

∛(5/3) =
∛45/3 ≈ 1.1856

Real cube root: the only number whose cube is 5/3.

≈ — rounded to 4 decimal places. 5/3 is not the cube of a rational number, so ∛(5/3) is irrational: its decimal expansion never ends and never repeats.

Root of a fraction
∛(5/3) = ∛5/∛3
Multiply by ∛(3²) = ∛9
∛5/∛3 = ∛45/∛27 = ∛45/3 ≈ 1.1856

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1.4≈ 1.1187
1.5≈ 1.1447
3/2∛12/2 ≈ 1.1447
5/3∛45/3 ≈ 1.1856
1.7281.2
2≈ 1.2599
2.1971.3

FAQ

What is the cube root of 5/3?

∛(5/3) = ∛45/3 ≈ 1.1856

Why is ∛(5/3) = ∛45/3?

∛(5/3) = ∛5/∛3. Multiplying the numerator and the denominator by ∛(3²) = ∛9 makes the denominator a perfect cube: ∛45/∛27 = ∛45/3. The value does not change; only the root leaves the denominator.

Is ∛(5/3) a rational number?

No: 5/3 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 ∛(5/3) is irrational; its decimal never ends and never repeats: ∛(5/3) ≈ 1.1856.

See Also