Cube Root of 0.3

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What is the cube root of 0.3?

Answer

∛0.3 ≈
0.6694

Real cube root: the only number whose cube is 0.3.

≈ — rounded to 4 decimal places. 0.3 is not the cube of a rational number, so ∛0.3 is irrational: its decimal expansion never ends and never repeats.

Between cubes
0.6³ = 0.216 < 0.3 < 0.343 = 0.7³, so 0.6 < ∛0.3 < 0.7 and ∛0.3 ≈ 0.6694

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
0.25≈ 0.63
1/4∛2/2 ≈ 0.63
8/272/3 ≈ 0.6667
0.3≈ 0.6694
1/3∛9/3 ≈ 0.6934
0.3430.7
343/10007/10 = 0.7

FAQ

What is the cube root of 0.3?

∛0.3 ≈ 0.6694

How to find ∛0.3 without a calculator?

Bracket it between cubes: 0.6³ = 0.216 < 0.3 < 0.343 = 0.7³, so ∛0.3 lies between 0.6 and 0.7. Narrowing the bracket digit by digit gives ∛0.3 ≈ 0.6694; 0.3 is not the cube of a decimal, so the root never ends.

Is ∛0.3 a rational number?

No: 0.3 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 ∛0.3 is irrational; its decimal never ends and never repeats: ∛0.3 ≈ 0.6694.

See Also