Cube Root of 0.08

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What is the cube root of 0.08?

Answer

∛0.08 ≈
0.4309

Real cube root: the only number whose cube is 0.08.

≈ — rounded to 4 decimal places. 0.08 is not the cube of a rational number, so ∛0.08 is irrational: its decimal expansion never ends and never repeats.

Between cubes
0.4³ = 0.064 < 0.08 < 0.125 = 0.5³, so 0.4 < ∛0.08 < 0.5 and ∛0.08 ≈ 0.4309

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FAQ

What is the cube root of 0.08?

∛0.08 ≈ 0.4309

How to find ∛0.08 without a calculator?

Bracket it between cubes: 0.4³ = 0.064 < 0.08 < 0.125 = 0.5³, so ∛0.08 lies between 0.4 and 0.5. Narrowing the bracket digit by digit gives ∛0.08 ≈ 0.4309; 0.08 is not the cube of a decimal, so the root never ends.

Is ∛0.08 a rational number?

No: 0.08 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 ∛0.08 is irrational; its decimal never ends and never repeats: ∛0.08 ≈ 0.4309.