Final answer:
Active transport is the process that moves ions across the cell membrane against the gradient, using cellular energy.
Step-by-step explanation:
The process responsible for moving nutrient ions across the cell membrane of plant root hairs when they are in lower concentrations in the groundwater compared to inside the cells is active transport.
Active transport is a mechanism that involves the cell expending energy (usually in the form of ATP) to move these ions against their concentration gradient, from an area of lower concentration to an area of higher concentration.
This is necessary because nutrients are often more concentrated within the plant cells than in the surrounding soil or water, and simply diffusing or moving down the concentration gradient would not suffice to nourish the plants.