Cube Root of 1200
Cube Root Calculator
What is the cube root of 1,200?
Answer
∛1,200 =
2∛150 ≈ 10.6266
Real cube root: the only number whose cube is 1,200.
≈ — rounded to 4 decimal places. 1,200 is not the cube of a rational number, so ∛1,200 is irrational: its decimal expansion never ends and never repeats.
- Prime factors
- 1,200 = (2 × 2 × 2) × 2 × 3 × 5 × 5 = 2⁴ × 3 × 5²
- Take out of the root
- ∛1,200 = ∛(2³ × 150) = 2∛150
- Between cubes
- 10³ = 1,000 < 1,200 < 1,331 = 11³, so 10 < ∛1,200 < 11 and ∛1,200 ≈ 10.6266
Related Calculations
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
Cube roots of nearby values
FAQ
What is the cube root of 1,200?
∛1,200 = 2∛150 ≈ 10.6266
How to simplify ∛1,200?
Factor 1,200 into primes: 1,200 = 2 × 2 × 2 × 2 × 3 × 5 × 5. Each triple of equal factors is a cube and comes out of the root as one factor; the rest stays under it: ∛1,200 = ∛(2³ × 150) = 2∛150.
Is ∛1,200 a rational number?
No: 1,200 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 ∛1,200 is irrational; its decimal never ends and never repeats: ∛1,200 ≈ 10.6266.
See Also
- Cube Root of 997 (∛997): Exact Value and Decimal
- Cube Root of 998 (∛998): Exact Value and Decimal
- Cube Root of 999 (∛999): Exact Value and Decimal
- Cube Root of 1000 (∛1000): Exact Value and Decimal
- Cube Root of 1001 (∛1001): Exact Value and Decimal
- Cube Root of 1024 (∛1024): Exact Value and Decimal
- Cube Root of 1029 (∛1029): Exact Value and Decimal
- Cube Root of 1080 (∛1080): Exact Value and Decimal
- Cube Root of 1089 (∛1089): Exact Value and Decimal
- Cube Root of 1125 (∛1125): Exact Value and Decimal
- Cube Root of 1210 (∛1210): Exact Value and Decimal
- Cube Root of 1225 (∛1225): Exact Value and Decimal
- Cube Root of 1280 (∛1280): Exact Value and Decimal
- Cube Root of 1296 (∛1296): Exact Value and Decimal
- Cube Root of 1323 (∛1323): Exact Value and Decimal
- Cube Root of 1331 (∛1331): Exact Value and Decimal
- Cube Root of 1332 (∛1332): Exact Value and Decimal
- Cube Root of 1369 (∛1369): Exact Value and Decimal
- Cube Root of 1372 (∛1372): Exact Value and Decimal
- Cube Root of 1458 (∛1458): Exact Value and Decimal
- Кубический корень из 1200 (∛1200): точное значение
- Raíz cúbica de 1200 (∛1200): valor exacto y decimal
- Raiz cúbica de 1200 (∛1200): valor exato e decimal