Cube Root of 39000
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What is the cube root of 39,000?
Answer
∛39,000 =
10∛39 ≈ 33.9121
Real cube root: the only number whose cube is 39,000.
≈ — rounded to 4 decimal places. 39,000 is not the cube of a rational number, so ∛39,000 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 39,000 = (2 × 2 × 2) × 3 × (5 × 5 × 5) × 13 = 2³ × 3 × 5³ × 13
- Take out of the root
- ∛39,000 = ∛(2³ × 5³ × 39) = 2 × 5 × ∛39 = 10∛39
- Between cubes
- 33³ = 35,937 < 39,000 < 39,304 = 34³, so 33 < ∛39,000 < 34 and ∛39,000 ≈ 33.9121
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- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Prime Factorization - Prime Factorization Calculator
- 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 39,000?
∛39,000 = 10∛39 ≈ 33.9121
How to simplify ∛39,000?
Factor 39,000 into primes: 39,000 = 2 × 2 × 2 × 3 × 5 × 5 × 5 × 13. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛39,000 = ∛(2³ × 5³ × 39) = 10∛39.
Is ∛39,000 a rational number?
No: 39,000 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 ∛39,000 is irrational; its decimal never ends and never repeats: ∛39,000 ≈ 33.9121.
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