Which tool would be used to smooth rough edges on wood?

The router is an excellent tool for smoothing rough edges on wood due to its design and functionality. It utilizes a rotating cutting bit that can easily and precisely shape the edges of wood, allowing for a smoother finish as it removes material along the edge. Routers can be adjusted to various depths and are pivotal in achieving detailed profiles or rounded edges on woodworking projects.

While chisels, files, and sandpaper can also be used in the finishing process, they serve distinctly different purposes and may not achieve the same level of edge smoothing that routers do. Chisels are primarily designed for carving and shaping but do not provide the same consistent finish. Files are used for finer shaping and smoothing but are typically more suited for metal or when a more precise edge is needed on smaller areas. Sandpaper is great for overall surface smoothing but may not be as efficient as a router for edge profiling tasks. Thus, the router is specifically crafted for the smoothing of edges with versatility and precision unmatched by the other tools listed.