Cube Root of 3

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Cube root of

What is the cube root of 3?

Answer

∛3 ≈
1.4422

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

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

Prime factors
3 is a prime number: no triple of equal factors.
Between cubes
1³ = 1 < 3 < 8 = 2³, so 1 < ∛3 < 2 and ∛3 ≈ 1.4422

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2.7≈ 1.3925
2.7441.4
2.8≈ 1.4095
3≈ 1.4422
27/83/2 = 1.5
3.3751.5
4≈ 1.5874

FAQ

What is the cube root of 3?

∛3 ≈ 1.4422

Can ∛3 be simplified?

No: no prime appears three times in 3, so its only cube factor is 1 and ∛3 is already in simplest form. Since 1³ = 1 < 3 < 8 = 2³, ∛3 lies between 1 and 2: ∛3 ≈ 1.4422.

Is ∛3 a rational number?

No: 3 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 is irrational; its decimal never ends and never repeats: ∛3 ≈ 1.4422.

See Also