I'm sorry Jae. Referring to the WesternGarden book on the shelf - Perhaps the root-store was not damaged, and only the root-tips-feed area is damaged. Not a great situation, but the root-store might keep the tree thriving through the summer and autumn. Anyway, if you have the WesternGarden book, I'm looking at the "basic planting and care" section, "how plants grow" subsection.
And along the lines of this project, I live in a city where the city "owns" the trees on the verge, but I am responsible for the sidewalk being smooth and flat. I cannot prune, or touch the tree. Should the city's trees damage the pavement, I have the honor of paying at least 50% of repairs. After some 10 years of repeated damage, I have the honor of paying for the removal of the city tree! And now the kicker - the contractor the city use to "repair" the pavement just cut the root-tips area - just whack away at them, literally - no concern at all for the health of the tree. Ugh.