Answer
If there was a beating cilia on the surface of the cell, it would be eukaryotic.
Work Step by Step
One could also discern if it was a eukaryotic cell by watching the cell divide. If mitotic chromosomes were present, this would also mean the cell was eukaryotic. If you dyed the cell and a nucleus become visible, it would be eukaryotic. If the nucleus was absent however, it would be possible the cell is an archaeon (prokaryote). If it was stained with Gram stain, one could tell if some molecules present in bacteria could be found. If all else fails, one could analyze the DNA and RNA. If these cannot be found, it is more than likely just dirt.
