The surface is likely smooth - although perhaps not with the best UV isocurve orientation (made with Sweep 2 rails? Loft?) - the problem you are seeing is elsewhere. The images I suspect are made with flat shading on, showing the display mesh triangles…
3D printing requires you to export an .stl file, that is to say a mesh representation of your smooth NURBS surfaces. The settings you use to export the file will determine how fine the facets are in the final 3D printed object. Too coarse, and they will show up in the 3D print.
Plus, I have a feeling from the picture of your 3D print that your object is far from the origin, this will cause jagged meshes and bad .stls. Check that as well and if that is the case, move the object close to the origin before exporting the .stl.
Feel free to post the .3dm here if you want someone to check.