Step 1: Understanding the Concept
Root hairs are tubular outgrowths of single epiblema cells. They are unicellular, unbranched and thin-walled.
Step 2: Check each statement
Cytoplasmic extensions of epiblema cells, unbranched and very delicate are all correct.
Step 3: Incorrect one
Root hairs live only a few days. Old hairs die and new ones form behind the growing tip, so they are not permanent.
Final Answer:
The incorrect statement is that root hairs are permanent.
\[ \boxed{\text{(D) }\text{They are permanent.}} \]