Scrub-a-Dub-Dub... Bottle brush won't reach all the way down to scrub that dirty glass or plastic vase?
Put 2 tablespoons of dry rice inside, then pour in 1/2 cup of hot, soapy water. Cover with the palm of your hand and shake vigorously. Discard rice and rinse the now-sparkling vase.
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When it comes to cleaning items around the house, I generally have a separate set of tools for each category: sponge and scrubber just for dishes, sponge and scrubber (and often store-brand magic eraser!) for the sink, sponge for pet carriers, etc.