Might be some Hornwart? Look up Hornwart and see if it matches
This is commonly sold as "Frill" at your LFS.
If you plant it now, the bottom may start to die off. A lot of people just pinch the bottom "stemmy" portions off and replant the tops. I stick the stemmy portion in the substrate and often it grows new plants. I mix mine with Cabomba (and replant the same way). Needs a decent amount of light to grow and that is likely why LFS guy told you to let it float. You can plant it now, or, if it floats for a week or two it may grow roots for you (roots could start growing well above the base --- similar to how anacharis grows).
Go ahead and plant roots if you like...This plant is really an invasive weed in the southeastern U.S., but makes for a nice aquarium plant. It does need a decent amount of light (~2 watts/gallon). As it grows, just pinch off rooted parts and replant. I plant the "stemmy" portions horizontally and occasionally new plants emerge. You can let it float for a few days and it may grow faster when you do plant it.
Okay I planted one of the plants that has roots do you think it will just continue growing tall? I don't know how many watts my light has though. I attached a picture of the plant and the light that I have. Thanks!