Cube Root of 6

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Cube root of

What is the cube root of 6?

Answer

∛6 ≈
1.8171

Real cube root: the only number whose cube is 6.

≈ — rounded to 4 decimal places. 6 is not the cube of a rational number, so ∛6 is irrational: its decimal expansion never ends and never repeats.

Prime factors
6 = 2 × 3
Take out of the root
No prime appears three times, so ∛6 is already in simplest form.
Between cubes
1³ = 1 < 6 < 8 = 2³, so 1 < ∛6 < 2 and ∛6 ≈ 1.8171

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
4.9131.7
5≈ 1.71
5.8321.8
6≈ 1.8171
6.8591.9
7≈ 1.9129
82

FAQ

What is the cube root of 6?

∛6 ≈ 1.8171

Can ∛6 be simplified?

No: no prime appears three times in 6, so its only cube factor is 1 and ∛6 is already in simplest form. Since 1³ = 1 < 6 < 8 = 2³, ∛6 lies between 1 and 2: ∛6 ≈ 1.8171.

Is ∛6 a rational number?

No: 6 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 ∛6 is irrational; its decimal never ends and never repeats: ∛6 ≈ 1.8171.

See Also