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What is the cube root of 2,300?

Answer

∛2,300 ≈
13.2001

Real cube root: the only number whose cube is 2,300.

≈ — rounded to 4 decimal places. 2,300 is not the cube of a rational number, so ∛2,300 is irrational: its decimal expansion never ends and never repeats.

Prime factors
2,300 = 2 × 2 × 5 × 5 × 23 = 2² × 5² × 23
Take out of the root
No prime appears three times, so ∛2,300 is already in simplest form.
Between cubes
13³ = 2,197 < 2,300 < 2,744 = 14³, so 13 < ∛2,300 < 14 and ∛2,300 ≈ 13.2001

Related Calculations

See Also

Recalculate with different values ↑

Cube roots of nearby values

N∛N
2,0242∛253 ≈ 12.6494
2,19713
2,2002∛275 ≈ 13.0059
2,300≈ 13.2001
2,4002∛300 ≈ 13.3887
2,4017∛7 ≈ 13.3905
2,450≈ 13.481

FAQ

What is the cube root of 2,300?

∛2,300 ≈ 13.2001

Can ∛2,300 be simplified?

No: no prime appears three times in 2,300, so its only cube factor is 1 and ∛2,300 is already in simplest form. Since 13³ = 2,197 < 2,300 < 2,744 = 14³, ∛2,300 lies between 13 and 14: ∛2,300 ≈ 13.2001.

Is ∛2,300 a rational number?

No: 2,300 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 ∛2,300 is irrational; its decimal never ends and never repeats: ∛2,300 ≈ 13.2001.

See Also