Roundup is absorbed through the leaves of the plant...or the blades of grass. The leaves uptake the chemical that then inhibits protein production and kills the weed/plant. It is not taken-up by the root system, though it will eventually get to the root system as it travels through the xylem and phloem.
So, around the base of a tree, you could douse the grass/weeds and it will have ZERO adverse impact on the tree. You could pour 5 gallons of roundup on a tree trunk or exposed roots and nothing would happen. The only way it might affect a tree is if you doused the entire canopy of the tree continuously with lots or roundup. Even if you get a little drift while spraying the ground, you will be just fine.
So, spray away.