Question

Calcula y Simplifica:
$\sqrt[3]{16}+2 \sqrt[3]{2}- \sqrt[3]{54} - \frac{21}{5} \sqrt[3]{250}$

Answer 1

Tenemos.

16 = 2 * 2 * 2 * 2 = 2³ * 2
54 = 3 * 3 * 3 * 2 = 3³ * 2
250 = 2 * 5 * 5 *5  = 2 * 5³

∛16 + 2∛2 - ∛54 - 21/5 ∛250 =
∛(2³ * 2) + 2∛2 - ∛(3³ * 2) - 21/5∛(2 * 5³) =  Aplicas √(a*b) =√a * √b
∛2³ * ∛2 + 2∛2 - ∛3³ * ∛2 - 21/5 ∛5³ * ∛2 =    Aplicando ∛a = a¹/³
2³/³∛2  + 2∛2 - 3³/³∛2 - 21/5 *5³/³∛2 =
2∛2 + 2∛2 - 3∛2 - 21/5 * 5∛2 =
4∛2 - 3∛2 - 21∛2 =
∛2 - 21∛2 =
-20∛2

Respuesta.
- 20∛2

Answer 2

$\sqrt[3]{16} = \sqrt[3]{2. 2^{3} } =2 \sqrt[3]{2}$ 

$\sqrt[3]{54} = \sqrt[3]{2. 3^{3} } =3 \sqrt[3]{2}$

$\frac{21}{5} \sqrt[3]{250} = \frac{21}{5} \sqrt[3]{ 2. 5^{3} } = \frac{21.5}{5} \sqrt[3]{2} =21 \sqrt[3]{2}$

$2 \sqrt[3]{2} +2 \sqrt[3]{2} - 3\sqrt[3]{2} -21 \sqrt[3]{2}$

$- 20\sqrt[3]{2}$