How do gases enter the root system of a plant?
The root system of a plant provides anchorage into its substrate--(soil) but it is also responsible for absorption of water and specific nutrients necessary for plant growth.
Roots may have extra projections known as root hairs which are thin and allow for the diffusion of important chemicals across their membranes. Root hairs increase the surface area for absorption of materials into a plant. After water and nutrients are absorbed by the hairs, the water is transported upward via special vascular (conducting) tissue known as xylem cells and transported to the rest of the plant.
Some roots are capable of exchanging gases due to the presence of lenticels-- or pores, especially if these are in plants that are adapted to a watery environment like a swamp and the roots are above the ground. In order for plants to utilized the stored chemical energy they have made by the process of photosynthesis, oxygen is needed to carry out aerobic respiration. Some of that chemical energy is stored in roots as sugar or starch. Since the soil has air spaces, oxygen can easily be absorbed by root hairs and lenticels directly from the soil and then used by root cells in the process of respiration.