Cube Root of 152
Cube Root Calculator
What is the cube root of 152?
Answer
∛152 =
2∛19 ≈ 5.3368
Real cube root: the only number whose cube is 152.
≈ — rounded to 4 decimal places. 152 is not the cube of a rational number, so ∛152 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 152 = (2 × 2 × 2) × 19 = 2³ × 19
- Take out of the root
- ∛152 = ∛(2³ × 19) = 2∛19
- Between cubes
- 5³ = 125 < 152 < 216 = 6³, so 5 < ∛152 < 6 and ∛152 ≈ 5.3368
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- Scientific Calculator with Memory & History - Free Engineering Calculator Online with Memory Function, Operation History, Logarithms & Trigonometry. Similar to ti-83, ti-84, ti-89
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FAQ
What is the cube root of 152?
∛152 = 2∛19 ≈ 5.3368
How to simplify ∛152?
Factor 152 into primes: 152 = 2 × 2 × 2 × 19. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛152 = ∛(2³ × 19) = 2∛19.
Is ∛152 a rational number?
No: 152 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 ∛152 is irrational; its decimal never ends and never repeats: ∛152 ≈ 5.3368.
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