Cube Root of 5/2

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What is the cube root of 5/2?

Answer

∛(5/2) =
∛20/2 ≈ 1.3572

Real cube root: the only number whose cube is 5/2.

≈ — rounded to 4 decimal places. 5/2 is not the cube of a rational number, so ∛(5/2) is irrational: its decimal expansion never ends and never repeats.

5/2 = 2.5.

Root of a fraction
∛(5/2) = ∛5/∛2
Multiply by ∛(2²) = ∛4
∛5/∛2 = ∛20/∛8 = ∛20/2 ≈ 1.3572

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2.1971.3
2.25≈ 1.3104
2.5≈ 1.3572
5/2∛20/2 ≈ 1.3572
2.7≈ 1.3925
2.7441.4
2.8≈ 1.4095

FAQ

What is the cube root of 5/2?

∛(5/2) = ∛20/2 ≈ 1.3572

Why is ∛(5/2) = ∛20/2?

∛(5/2) = ∛5/∛2. Multiplying the numerator and the denominator by ∛(2²) = ∛4 makes the denominator a perfect cube: ∛20/∛8 = ∛20/2. The value does not change; only the root leaves the denominator.

Is ∛(5/2) a rational number?

No: 5/2 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 ∛(5/2) is irrational; its decimal never ends and never repeats: ∛(5/2) ≈ 1.3572.

See Also