Cube Root of 3/2

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What is the cube root of 3/2?

Answer

∛(3/2) =
∛12/2 ≈ 1.1447

Real cube root: the only number whose cube is 3/2.

≈ — rounded to 4 decimal places. 3/2 is not the cube of a rational number, so ∛(3/2) is irrational: its decimal expansion never ends and never repeats.

3/2 = 1.5.

Root of a fraction
∛(3/2) = ∛3/∛2
Multiply by ∛(2²) = ∛4
∛3/∛2 = ∛12/∛8 = ∛12/2 ≈ 1.1447

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
4/3∛36/3 ≈ 1.1006
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

FAQ

What is the cube root of 3/2?

∛(3/2) = ∛12/2 ≈ 1.1447

Why is ∛(3/2) = ∛12/2?

∛(3/2) = ∛3/∛2. Multiplying the numerator and the denominator by ∛(2²) = ∛4 makes the denominator a perfect cube: ∛12/∛8 = ∛12/2. The value does not change; only the root leaves the denominator.

Is ∛(3/2) a rational number?

No: 3/2 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 ∛(3/2) is irrational; its decimal never ends and never repeats: ∛(3/2) ≈ 1.1447.

See Also