AHSME 1961 Problem 12

The first three terms of a geometric progression are $\sqrt{2}, \sqrt[3]{2}, \sqrt[6]{2}$. Find the fourth term. $\textbf{(A)}\ 1 \textbf{(B)}\ \sqrt[7]{2} \textbf{(C)}\ \sqrt[8]{2} \textbf{(D)}\ \sqrt[9]{2} \textbf{(E)}\ \sqrt[10]{2}$