Cube Root of 7290
Cube Root Calculator
What is the cube root of 7,290?
Answer
∛7,290 =
9∛10 ≈ 19.3899
Real cube root: the only number whose cube is 7,290.
≈ — rounded to 4 decimal places. 7,290 is not the cube of a rational number, so ∛7,290 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 7,290 = 2 × (3 × 3 × 3) × (3 × 3 × 3) × 5 = 2 × 3⁶ × 5
- Take out of the root
- ∛7,290 = ∛((3³)² × 10) = 3² × ∛10 = 9∛10
- Between cubes
- 19³ = 6,859 < 7,290 < 8,000 = 20³, so 19 < ∛7,290 < 20 and ∛7,290 ≈ 19.3899
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See Also
- 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
Cube roots of nearby values
| N | ∛N |
|---|---|
| 5,488 | 14∛2 ≈ 17.6389 |
| 5,832 | 18 |
| 6,859 | 19 |
| 7,290 | 9∛10 ≈ 19.3899 |
| 7,776 | 6∛36 ≈ 19.8116 |
| 8,000 | 20 |
| 8,788 | 13∛4 ≈ 20.6362 |
FAQ
What is the cube root of 7,290?
∛7,290 = 9∛10 ≈ 19.3899
How to simplify ∛7,290?
Factor 7,290 into primes: 7,290 = 2 × 3 × 3 × 3 × 3 × 3 × 3 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛7,290 = ∛((3³)² × 10) = 9∛10.
Is ∛7,290 a rational number?
No: 7,290 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 ∛7,290 is irrational; its decimal never ends and never repeats: ∛7,290 ≈ 19.3899.
See Also
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