The value of ( 8 )^1/3 is = ?

Answer: Option C

$$\begin{array}{rl}& {\left(\sqrt{8}\right)}^{\frac{1}{3}}\\ & ={\left(8^{\frac{1}{2}}\right)}^{\frac{1}{3}}\\ & =8^{\left(\frac{1}{2}\times \frac{1}{3}\right)}\\ & =8^{\frac{1}{6}}\\ & ={\left(2^3\right)}^{\frac{1}{6}}\\ & =2^{\left(3\times \frac{1}{6}\right)}\\ & =2^{\frac{1}{2}}\\ & =\sqrt{2}\end{array}$$