Cube Root of 1024
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What is the cube root of 1,024?
Answer
∛1,024 =
8∛2 ≈ 10.0794
Real cube root: the only number whose cube is 1,024.
≈ — rounded to 4 decimal places. 1,024 is not the cube of a rational number, so ∛1,024 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,024 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 2 = 2¹⁰
- Take out of the root
- ∛1,024 = ∛((2³)³ × 2) = 2³ × ∛2 = 8∛2
- Between cubes
- 10³ = 1,000 < 1,024 < 1,331 = 11³, so 10 < ∛1,024 < 11 and ∛1,024 ≈ 10.0794
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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 1,024?
∛1,024 = 8∛2 ≈ 10.0794
How to simplify ∛1,024?
Factor 1,024 into primes: 1,024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,024 = ∛((2³)³ × 2) = 8∛2.
Is ∛1,024 a rational number?
No: 1,024 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 ∛1,024 is irrational; its decimal never ends and never repeats: ∛1,024 ≈ 10.0794.
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