Use the properties of radicals to rewrite the numbers.
[tex]\begin{gathered} \sqrt[]{8}=\sqrt[]{4\cdot2} \\ =\sqrt[]{4}\cdot\sqrt[]{2} \\ =2\cdot\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} \frac{\sqrt[]{16}}{2}=\frac{4}{2} \\ =2 \end{gathered}[/tex]It is a known fact that:
[tex]1<\sqrt[]{2}[/tex]Multiply both sides of the inequality by 2:
[tex]2<2\cdot\sqrt[]{2}[/tex]Substitute for √8=2√2 and √16/2=2:
[tex]\frac{\sqrt[]{16}}{2}<\sqrt[]{8}[/tex]