Cube Root of 9999

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Cube root of

What is the cube root of 9,999?

Answer

∛9,999 ≈
21.5436

Real cube root: the only number whose cube is 9,999.

≈ — rounded to 4 decimal places. 9,999 is not the cube of a rational number, so ∛9,999 is irrational: its decimal expansion never ends and never repeats.

Prime factors
9,999 = 3 × 3 × 11 × 101 = 3² × 11 × 101
Take out of the root
No prime appears three times, so ∛9,999 is already in simplest form.
Between cubes
21³ = 9,261 < 9,999 < 10,648 = 22³, so 21 < ∛9,999 < 22 and ∛9,999 ≈ 21.5436

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
8,78813∛4 ≈ 20.6362
9,26121
9,621≈ 21.2687
9,999≈ 21.5436
10,00010∛10 ≈ 21.5443
10,36812∛6 ≈ 21.8054
10,64822

FAQ

What is the cube root of 9,999?

∛9,999 ≈ 21.5436

Can ∛9,999 be simplified?

No: no prime appears three times in 9,999, so its only cube factor is 1 and ∛9,999 is already in simplest form. Since 21³ = 9,261 < 9,999 < 10,648 = 22³, ∛9,999 lies between 21 and 22: ∛9,999 ≈ 21.5436.

Is ∛9,999 a rational number?

No: 9,999 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 ∛9,999 is irrational; its decimal never ends and never repeats: ∛9,999 ≈ 21.5436.

See Also