AMC 8 2017 Problem 3

What is the value of the expression $\sqrt{16\sqrt{8\sqrt{4}}}$ ? $\textbf{(A) }4 \textbf{(B) }4\sqrt{2} \textbf{(C) }8 \textbf{(D) }8\sqrt{2} \textbf{(E) }16$