Dont put expensive items like t.v.'s in the rooms that are being renovated! I've worked on a number of building sites and the dust is a constant problem and extremely difficult to control. One method used on large sites (with concrete floors) is do dampen the area, i.e. hose it down with water, just enough that the floor is wet and not flooded. Then sweep up. This will stop the dust flying around the air when you sweep up. I don't know if your property will lend itself to this method. But, I'm sorry to say, you will struggle to get it dust free, and you will have to clean it, and clean it again, and clean it again, and.... you get the idea. That is why construction sites employ labourers to clean up constantly, all day every day, and they're still a mess.