Step 1: Picture a cross section of a dicot root.
Moving from outside in, the tissue layers are arranged as epidermis, cortex, endodermis, pericycle, and then the vascular tissue at the centre.
Step 2: Eliminate the inner layers.
Endodermis and pericycle both sit deep inside, just around the vascular bundle, so neither can be the outermost covering. Cortex lies between the epidermis and endodermis, again not the true outer boundary.
Step 3: Confirm the outermost layer.
The single outermost layer of cells, which is in direct contact with the soil and often bears root hairs, is the epidermis (also called the piliferous layer in roots).
\[ \boxed{\text{Epidermis}} \]