Yes, the Islamic way of purifying things is to wash them thrice. First make sure that there are no impurities left, then wash three times and dry after each wash.
Clothes, sheets, prayer mats etc can be washed in the machine, and as for the floor and things other than clothes, pour water and wipe them dry with a clean towel or cloth, again pour water and wipe them dry with another clean towel, once again pour water for the third time and wipe them dry for the third time. Then wash those towels later on.
Follow the same procedure for a carpet if required. Clean impurities first then pour water on the impure area and use a towel or cloth to absorb it. Repeat the same procedure three times.