Final answer:
The root operation used to completely remove tonsils using a wire snare is Excision.
Step-by-step explanation:
The root operation that would be used to locate the procedure of completely removing tonsils by the use of a wire snare is Excision.
Excision refers to the cutting out or off, without any replacement, all of a body part. In this case, the tonsils are being completely removed without any replacement.
The other options, Extraction, Resection, and Repair, do not accurately describe the removal process of the tonsils.