Making an object smooth

I’m making this vase and I used the multiresolution modifier to smooth it out. It looks fine everywhere except the bottom. What’s happening there?

You either have lots of triangles or a face with more than 4 sides. Use quads when you have a non planar surface

Okay, I got rid of the circle at the bottom because it had more than 4 sides. I was able to smooth it out and attach another piece to the bottom. It looks better now, but why exactly does that happen? Does the multiresolution tool just not work for objects with more than 4 sides? Are there any other simple methods for smoothing objects? I just started using blender and am not very familiar with the different tools.