Are you sure that this plant is a water fern? It seems rather a Lemnoideae species (Araceae), probabily a species of Spirodela. It could be Spirodela oligorhiza.
The size, thickness, the shade of green above and the purple on the undersurface of the thalli in the photographs all indicate Spirodela. I considered S. punctata (Syn. Landoltia punctata) but the thalli in the photographs are too large and not elongated enough. That leaves Spirodela polyrhiza, so I agree with Jacek Drobnik. S. polyrhiza can have up to nine roots per thallus, but the smaller number in the photographs could be simply due to damage when sampling, or perhaps it's just an atypical population.
I could not understand this question of Misty Walker. Ferns are primitive groups of plants which reproduce by means of spores which are produced on leaves. They do not produce flowers, fruits and seeds for reproduction.
Angiosperms are those plants produce flowers, fruits and seeds for reproduction.
But there are flowering plants which looks like ferns in shape of leavews. A good example is Pteridophyllum racemosum, where the leaf look like that of a Fern. But it produces flowers, fruits and seeds as any other Flowering plant.
A fern always is a fern and a flowering plant always is a flowering plant.
I agree with Mehdi, it is a Lemna because of having only one root per thallus and having roots (vs. Wolffia and Wolffiella). That it is L. gibba is different matter.