How do the tiny root hairs work?
The tiny root hairs work by a process called Osmosis. In a nutshell, osmosis is the flow of a liquid of lower concentration, through a semi-permeable membrane, to try to dilute a liquid of higher concentration on the other side of the membrane. In the case of roots, the liquid of lower concentration is your nutrient solution, the semi-permeable membrane is the root hair wall, and the liquid of higher concentration that is being diluted is the complex aqueous mixture of sugars and starches within the root cells themselves.