Answer
$\sqrt 2$
Work Step by Step
We know from the radical form of $a^{\frac{m}{n}}$ that $a^{\frac{m}{n}}=\sqrt[n] a^{m}$ (where the indicated roots are real numbers).
Therefore, $\sqrt[6] 8=\sqrt[6] 2^{3}=2^{\frac{3}{6}}=2^{\frac{1}{2}}=\sqrt 2$.