Mipmapping needs more ram. I saw elsewhere that it would work out to about *1.3 not *1.5 - but I could be wrong. You basically divide the dimensions by 2 each time until it gets down to like 1x1. There is a little bit of overhead probably for storing the textures in an mipmap array.
Filtering does not use any additional video ram.
Filtering does not use any additional video ram.