Can washing of produce help get rid of pesticides? Not really. The fruits and vegetables tested by the USDA PDP (*) are prepared emulating the practices of the average consumer before testing for pesticides. That is: (1) apples are washed with stems and cores removed; (2) asparagus and spinach have inedible portions removed and are washed; (3) cantaloupes are cut in half and seed and rinds are removed; [...] and (9) tomatoes are washed and stems removed.
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Washing before consuming is highly recommended because helps decrease the pesticide residues present on the surface of the vegetables, but the majorities of pollutants are absorbed into the plant and can't be just washed away. Some pesticides are specifically created to stick to the surface of the crops and they don't come out by washing. Peeling can help eliminating some of the chemicals but not all, and a lot of important substances will be discarded with the skin.
So, on one hand we have to eat plenty of fruit and vegetables for a healthy diet, and on the other hand we have to reduce as much a possible the intake of pesticides. What to do if you are unconvinced by the claims of the chemical companies that certain levels of pesticides are not dangerous?