Cube Root of 999

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Cube root of

What is the cube root of 999?

Answer

∛999 =
3∛37 ≈ 9.9967

Real cube root: the only number whose cube is 999.

≈ — rounded to 4 decimal places. 999 is not the cube of a rational number, so ∛999 is irrational: its decimal expansion never ends and never repeats.

Prime factors
999 = (3 × 3 × 3) × 37 = 3³ × 37
Take out of the root
∛999 = ∛(3³ × 37) = 3∛37
Between cubes
9³ = 729 < 999 < 1,000 = 10³, so 9 < ∛999 < 10 and ∛999 ≈ 9.9967

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See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
925≈ 9.7435
997≈ 9.99
998≈ 9.9933
9993∛37 ≈ 9.9967
1,00010
1,001≈ 10.0033
1,0248∛2 ≈ 10.0794

FAQ

What is the cube root of 999?

∛999 = 3∛37 ≈ 9.9967

How to simplify ∛999?

Factor 999 into primes: 999 = 3 × 3 × 3 × 37. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛999 = ∛(3³ × 37) = 3∛37.

Is ∛999 a rational number?

No: 999 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 ∛999 is irrational; its decimal never ends and never repeats: ∛999 ≈ 9.9967.

See Also