Lets start by factoring the 216 into its smaller parts.
[tex]\sqrt[3]{2 * 2 * 2 * 3 * 3 * 3}[/tex]
From here, we can separate the three 2s and the three 3s into two separate radicals.
[tex]\sqrt[3]{2*2*2} * \sqrt[3]{3*3*3} [/tex]
Since we have three copies of the same number in each, the answer to the cube root is the number we have the copies of.
[tex] \sqrt[3]{2*2*2} * \sqrt[3]{3*3*3} = 2 * 3[/tex]
Finally, we just need to multiply out what remains to find the solution.
[tex]2*3 = 6[/tex]
So, the final answer is 6.
