C.H.
Hi J.,
I was told that when tree roots are very close to the surface it is because they are trying to get to water. Your trees roots are sprouting little "suckers" because they are stressed. When watering a tree it is important that it be watered deeply, that way the roots will move down toward the deeper watering. Since there are also grass and plantings you may be judging the amount of needed water by the landscaping plants vigor. Since the landscape plants roots are nearer the surface they get water first. Water the trees in the evening for perhaps an hour so the heat/sun doesn't cause the water to evaporate before it can get to the lower roots. Over time--maybe a whole season--the tree roots will grow deeper as their water needs are met. If there is a street or driveway nearby, that will hold heat and make the surface water evaporate more quickly as well. Check with a tree nurseryman who might suggest fertilization or mulch requirements. HTH