Urban guy, I bet everyone who viewed this post felt bad for you. The first picture is worth a thousand words. Your dog looked many times happier than you. Good thing is now ya know there is a better way. Next spring if ya keep the new sprouting pads from reaching the surface they will die.
As for the Beaver root, I like that. Earlier this summer I helped my son eradicate lots of pads. Couple of weeks later he started to hand pick the roots out. He asked if all aquatic plants had roots made of lead.