For example if the keyword is: test will the ad show for search phrases: testing test's testtt tetest tests
It might but not for all your variations. Google will expand (their term), broad matched keywords. By this they mostly mean using synonyms but also some plurals. Therefore, they might expand test to trial, experiment, evaluation and possibly tests. But for sure, "dog food" to "canine nourishment". Your testtt example might be covered as it is not a real word and Google would ask the searcher "did you mean test?". testing and test's, I'm not sure. tetest probably not unless Google figures the searcher meant test. I know also they will "skrink" broad keywords. By that, I mean your ads might trigger simply because your keyword contains a word also found in the search term. Real-life example I've seen: keyword "nursing job at hospital" could trigger for a search on "mycity general hospital address". Search has nothing to do with the theme but was triggered just because of the word hospital. That's why I stay away from broad matches as much as possible. You just don't know what Google's thinking.
Thanks for the incredibly thorough response ! When I tried migrating from broad matches my traffic dropped very low, I'm going to try going through all the search phrases people have made and turning them into keywords to try and broaden my horizon.
If you're using broad match heavily, check your keyword reports every night and look for mismatches to add as negatives. Otherwise your CTR will be terrible and you'll waste a lot of money.
I partially agree with Psyonic. He's referring to the Search Query Report (SQR). Don't need to check every night unless you have tens of thousands of impressions every day. The idea is to have less broad matches, especially the two and three-word keywords, and use phrase and exact matches instead. The SQR can be a real eye-opener on how people search for your keywords. It is also good to weed out those broad matches, find potential negative as well as phrase and exact matches. Only problem is that SQR only reports on clicks your received but can still be very useful.