Cube Root of 5/4

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What is the cube root of 5/4?

Answer

∛(5/4) =
∛10/2 ≈ 1.0772

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

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

5/4 = 1.25.

Root of a fraction
∛(5/4) = ∛5/∛4
Multiply by ∛(4²) = ∛16
∛5/∛4 = ∛80/∛64 = ∛80/4
Take out of the root
∛80/4 = ∛(2³ × 10)/4 = 2∛10/4 = ∛10/2 ≈ 1.0772

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
1.2≈ 1.0627
1.21≈ 1.0656
1.25≈ 1.0772
5/4∛10/2 ≈ 1.0772
1.33≈ 1.0997
1.3311.1
4/3∛36/3 ≈ 1.1006

FAQ

What is the cube root of 5/4?

∛(5/4) = ∛10/2 ≈ 1.0772

Why is ∛(5/4) = ∛10/2?

∛(5/4) = ∛5/∛4. Multiplying the numerator and the denominator by ∛(4²) = ∛16 makes the denominator a perfect cube: ∛80/∛64 = ∛80/4. Taking the cubes out of ∛80 and reducing gives ∛10/2. The value does not change; only the root leaves the denominator.

Is ∛(5/4) a rational number?

No: 5/4 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 ∛(5/4) is irrational; its decimal never ends and never repeats: ∛(5/4) ≈ 1.0772.

See Also