Seems like a simple enough task but digging dandelions to get the roots out is easier to say than do. This root was "dug" with the Lee Valley water weeder. This tool shoots a strong stream of water down beside the dandelion root and in the end a very long root comes out. This dandelion is not likely to re-grow but it does take a lot of effort and water to remove a dandelion with this system.
Keep in mind that overuse of commercial fertilizers gradually reduces available Calcium (which is displaced off the clay particles by Pottasium and then leached). Low calcium levels are implicated in poor soil conditions and higher dandelion populations. Underuse of micro-organism stimulating organic matter can also lead to compacted dandelion-prone soil.