Final answer:
Inarching grafting is utilized to replace a damaged root system of a tree, using a healthy rootstock from another tree to merge with the host and establish a new root system.
Step-by-step explanation:
The type of grafting used to replace a damaged root system of a tree is inarching. In inarching, a healthy rootstock from another tree or seedling is grafted onto the damaged tree near the base, establishing a new root system that provides stability and nutrients as it grows and merges with the host.
This is an important horticultural technique for saving trees that have suffered root damage, ensuring their survival and continued growth.