Cube Root of 4500

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What is the cube root of 4,500?

Answer

∛4,500 =
5∛36 ≈ 16.5096

Real cube root: the only number whose cube is 4,500.

≈ — rounded to 4 decimal places. 4,500 is not the cube of a rational number, so ∛4,500 is irrational: its decimal expansion never ends and never repeats.

Prime factors
4,500 = 2 × 2 × 3 × 3 × (5 × 5 × 5) = 2² × 3² × 5³
Take out of the root
∛4,500 = ∛(5³ × 36) = 5∛36
Between cubes
16³ = 4,096 < 4,500 < 4,913 = 17³, so 16 < ∛4,500 < 17 and ∛4,500 ≈ 16.5096

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Cube roots of nearby values

N∛N
4,045≈ 15.9333
4,09616
4,225≈ 16.1662
4,5005∛36 ≈ 16.5096
4,900≈ 16.985
4,91317
5,382≈ 17.5246

FAQ

What is the cube root of 4,500?

∛4,500 = 5∛36 ≈ 16.5096

How to simplify ∛4,500?

Factor 4,500 into primes: 4,500 = 2 × 2 × 3 × 3 × 5 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛4,500 = ∛(5³ × 36) = 5∛36.

Is ∛4,500 a rational number?

No: 4,500 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 ∛4,500 is irrational; its decimal never ends and never repeats: ∛4,500 ≈ 16.5096.

See Also