Cube Root of 12

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Cube root of

What is the cube root of 12?

Answer

∛12 ≈
2.2894

Real cube root: the only number whose cube is 12.

≈ — rounded to 4 decimal places. 12 is not the cube of a rational number, so ∛12 is irrational: its decimal expansion never ends and never repeats.

Prime factors
12 = 2 × 2 × 3 = 2² × 3
Take out of the root
No prime appears three times, so ∛12 is already in simplest form.
Between cubes
2³ = 8 < 12 < 27 = 3³, so 2 < ∛12 < 3 and ∛12 ≈ 2.2894

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
9.2612.1
10≈ 2.1544
11≈ 2.224
12≈ 2.2894
12.1672.3
13≈ 2.3513
14≈ 2.4101

FAQ

What is the cube root of 12?

∛12 ≈ 2.2894

Can ∛12 be simplified?

No: no prime appears three times in 12, so its only cube factor is 1 and ∛12 is already in simplest form. Since 2³ = 8 < 12 < 27 = 3³, ∛12 lies between 2 and 3: ∛12 ≈ 2.2894.

Is ∛12 a rational number?

No: 12 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 ∛12 is irrational; its decimal never ends and never repeats: ∛12 ≈ 2.2894.

See Also