unless you just walked in ten minutes ago, you know i spend a lot of time on waterbury reservoir, which, sadly, is an infested body of water. it has a number of invasive infestations both aquatic and terrestrial and i have both done my research and have blessing of management to conduct my small invasive abatement programs, which boil down to whenever i am staying on a campsite that is near an infestation (sometimes i choose a site based on an infestation) i spend a little time each day pulling and properly disposing of the invasive.
the department of forests, parks and recreation recommends this site: vermont invasives
so here are the two invasives i work with most:
what these two have in common is that although they will prefer to flower and seed, they will be happy to propagate and can send out new shoots and roots from ANY NODE, so any part of a stem floating around is a potential new infestation.
when you pull it, you have to be careful not to leave stray pieces floating around (particularly important with the naiad) and you have to make sure to dispose of the plants properly. if you have time, it's as easy as leaving the plants in a hostile environment until they are dry and dead. naiad simply needs to be pulled out on land where it can't grow and left somewhere it won't blow back into the water.
knotweed will be happy to grow in water or on land so any part you cut needs to be left in the sun and turned regularly until it turns brown and then you can drop it anywhere.
break up the root ball as much as you can and maybe hang it up in a tree to be sure.
knotweed are versatile and sneaky.