Cube Root of 1323
Cube Root Calculator
What is the cube root of 1,323?
Answer
∛1,323 =
3∛49 ≈ 10.9779
Real cube root: the only number whose cube is 1,323.
≈ — rounded to 4 decimal places. 1,323 is not the cube of a rational number, so ∛1,323 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,323 = (3 × 3 × 3) × 7 × 7 = 3³ × 7²
- Take out of the root
- ∛1,323 = ∛(3³ × 49) = 3∛49
- Between cubes
- 10³ = 1,000 < 1,323 < 1,331 = 11³, so 10 < ∛1,323 < 11 and ∛1,323 ≈ 10.9779
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 1,323?
∛1,323 = 3∛49 ≈ 10.9779
How to simplify ∛1,323?
Factor 1,323 into primes: 1,323 = 3 × 3 × 3 × 7 × 7. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,323 = ∛(3³ × 49) = 3∛49.
Is ∛1,323 a rational number?
No: 1,323 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 ∛1,323 is irrational; its decimal never ends and never repeats: ∛1,323 ≈ 10.9779.
See Also
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