The answer is [tex] 2\sqrt{2x}[/tex]
You're right about the x in the root not being able to simplify, but that just means that the x stays inside the square root. The 8 on the other hand simplifies to:
[tex] \sqrt{4*2} =2 \sqrt{2}[/tex]
So this means that [tex] \sqrt{8x} = 2\sqrt{2x}[/tex]