Cube Root of 5488
Cube Root Calculator
What is the cube root of 5,488?
Answer
∛5,488 =
14∛2 ≈ 17.6389
Real cube root: the only number whose cube is 5,488.
≈ — rounded to 4 decimal places. 5,488 is not the cube of a rational number, so ∛5,488 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 5,488 = (2 × 2 × 2) × 2 × (7 × 7 × 7) = 2⁴ × 7³
- Take out of the root
- ∛5,488 = ∛(2³ × 7³ × 2) = 2 × 7 × ∛2 = 14∛2
- Between cubes
- 17³ = 4,913 < 5,488 < 5,832 = 18³, so 17 < ∛5,488 < 18 and ∛5,488 ≈ 17.6389
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
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FAQ
What is the cube root of 5,488?
∛5,488 = 14∛2 ≈ 17.6389
How to simplify ∛5,488?
Factor 5,488 into primes: 5,488 = 2 × 2 × 2 × 2 × 7 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛5,488 = ∛(2³ × 7³ × 2) = 14∛2.
Is ∛5,488 a rational number?
No: 5,488 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 ∛5,488 is irrational; its decimal never ends and never repeats: ∛5,488 ≈ 17.6389.
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