Cube Root of 40

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Cube root of

What is the cube root of 40?

Answer

∛40 =
2∛5 ≈ 3.42

Real cube root: the only number whose cube is 40.

≈ — rounded to 4 decimal places. 40 is not the cube of a rational number, so ∛40 is irrational: its decimal expansion never ends and never repeats.

Prime factors
40 = (2 × 2 × 2) × 5 = 2³ × 5
Take out of the root
∛40 = ∛(2³ × 5) = 2∛5
Between cubes
3³ = 27 < 40 < 64 = 4³, so 3 < ∛40 < 4 and ∛40 ≈ 3.42

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
37≈ 3.3322
38≈ 3.362
39≈ 3.3912
402∛5 ≈ 3.42
41≈ 3.4482
42≈ 3.476
42.8753.5

FAQ

What is the cube root of 40?

∛40 = 2∛5 ≈ 3.42

How to simplify ∛40?

Factor 40 into primes: 40 = 2 × 2 × 2 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛40 = ∛(2³ × 5) = 2∛5.

Is ∛40 a rational number?

No: 40 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 ∛40 is irrational; its decimal never ends and never repeats: ∛40 ≈ 3.42.

See Also