Cube Root of 300

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Cube root of

What is the cube root of 300?

Answer

∛300 ≈
6.6943

Real cube root: the only number whose cube is 300.

≈ — rounded to 4 decimal places. 300 is not the cube of a rational number, so ∛300 is irrational: its decimal expansion never ends and never repeats.

Prime factors
300 = 2 × 2 × 3 × 5 × 5 = 2² × 3 × 5²
Take out of the root
No prime appears three times, so ∛300 is already in simplest form.
Between cubes
6³ = 216 < 300 < 343 = 7³, so 6 < ∛300 < 7 and ∛300 ≈ 6.6943

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
292≈ 6.6343
2962∛37 ≈ 6.6644
2973∛11 ≈ 6.6719
300≈ 6.6943
323≈ 6.8612
3243∛12 ≈ 6.8683
325≈ 6.8753

FAQ

What is the cube root of 300?

∛300 ≈ 6.6943

Can ∛300 be simplified?

No: no prime appears three times in 300, so its only cube factor is 1 and ∛300 is already in simplest form. Since 6³ = 216 < 300 < 343 = 7³, ∛300 lies between 6 and 7: ∛300 ≈ 6.6943.

Is ∛300 a rational number?

No: 300 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 ∛300 is irrational; its decimal never ends and never repeats: ∛300 ≈ 6.6943.

See Also