Cube Root of 150
Cube Root Calculator
What is the cube root of 150?
Answer
∛150 ≈
5.3133
Real cube root: the only number whose cube is 150.
≈ — rounded to 4 decimal places. 150 is not the cube of a rational number, so ∛150 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 150 = 2 × 3 × 5 × 5 = 2 × 3 × 5²
- Take out of the root
- No prime appears three times, so ∛150 is already in simplest form.
- Between cubes
- 5³ = 125 < 150 < 216 = 6³, so 5 < ∛150 < 6 and ∛150 ≈ 5.3133
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FAQ
What is the cube root of 150?
∛150 ≈ 5.3133
Can ∛150 be simplified?
No: no prime appears three times in 150, so its only cube factor is 1 and ∛150 is already in simplest form. Since 5³ = 125 < 150 < 216 = 6³, ∛150 lies between 5 and 6: ∛150 ≈ 5.3133.
Is ∛150 a rational number?
No: 150 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 ∛150 is irrational; its decimal never ends and never repeats: ∛150 ≈ 5.3133.
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