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Yes you should memorize the common strong bases and be able to recognize weak acids and bases, however it is more important to just know the strong ones. Then when you are finding a pH of a weak base or acid, you will need to use an ICE table.
For me, if the base contains an element in the first 2 columns of the periodic table and OH or an acid that contains an element in the halogen column, then its a strong acid/base and don't bother with the ice table. Anything else will not 100% dissociate and a ICE table is needed
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