Question

8 what is ∛288 expressed in simplest radical form? a 6∛9 b 8∛36 c 12∛2 d 2∛36

Explanation:

Step1: Factorizar 288

Descomponemos 288 en factores primos: $288 = 2\times144=2\times12\times12 = 2\times2\times6\times2\times6=2^5\times3^2$.

Step2: Reescribir la raíz cúbica

$\sqrt[3]{288}=\sqrt[3]{2^5\times3^2}=\sqrt[3]{2^3\times2^2\times3^2}$.

Step3: Sacar factores fuera de la raíz

$\sqrt[3]{2^3\times2^2\times3^2}=2\sqrt[3]{2^2\times3^2}=2\sqrt[3]{4\times9}=2\sqrt[3]{36}$.

Answer:

D. $2\sqrt[3]{36}$