Cube Root of 7776
Cube Root Calculator
What is the cube root of 7,776?
Answer
∛7,776 =
6∛36 ≈ 19.8116
Real cube root: the only number whose cube is 7,776.
≈ — rounded to 4 decimal places. 7,776 is not the cube of a rational number, so ∛7,776 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 7,776 = (2 × 2 × 2) × 2 × 2 × (3 × 3 × 3) × 3 × 3 = 2⁵ × 3⁵
- Take out of the root
- ∛7,776 = ∛(2³ × 3³ × 36) = 2 × 3 × ∛36 = 6∛36
- Between cubes
- 19³ = 6,859 < 7,776 < 8,000 = 20³, so 19 < ∛7,776 < 20 and ∛7,776 ≈ 19.8116
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 7,776?
∛7,776 = 6∛36 ≈ 19.8116
How to simplify ∛7,776?
Factor 7,776 into primes: 7,776 = 2 × 2 × 2 × 2 × 2 × 3 × 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: ∛7,776 = ∛(2³ × 3³ × 36) = 6∛36.
Is ∛7,776 a rational number?
No: 7,776 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 ∛7,776 is irrational; its decimal never ends and never repeats: ∛7,776 ≈ 19.8116.
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