Cube Root of 1296
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What is the cube root of 1,296?
Answer
∛1,296 =
6∛6 ≈ 10.9027
Real cube root: the only number whose cube is 1,296.
≈ — rounded to 4 decimal places. 1,296 is not the cube of a rational number, so ∛1,296 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,296 = (2 × 2 × 2) × 2 × (3 × 3 × 3) × 3 = 2⁴ × 3⁴
- Take out of the root
- ∛1,296 = ∛(2³ × 3³ × 6) = 2 × 3 × ∛6 = 6∛6
- Between cubes
- 10³ = 1,000 < 1,296 < 1,331 = 11³, so 10 < ∛1,296 < 11 and ∛1,296 ≈ 10.9027
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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 1,296?
∛1,296 = 6∛6 ≈ 10.9027
How to simplify ∛1,296?
Factor 1,296 into primes: 1,296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,296 = ∛(2³ × 3³ × 6) = 6∛6.
Is ∛1,296 a rational number?
No: 1,296 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 ∛1,296 is irrational; its decimal never ends and never repeats: ∛1,296 ≈ 10.9027.
See Also
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