So, you found them another variety of the salad buffet, hm?
Duckweed is indeed very good for goldfish, and easy to digest. I used to have a whole tub full of duckweed, before the last cooler winter wiped it all out. So hard to come by in Florida, since its considered an invasive weed here, and illegal to sell.
The little roots are showing that your plant is happy - and so much more. The roots are actually a little mini filtration system, they suck up waste and nitrates from the water. And yes, they can get quite long compared to the small leaves. Enjoy it while it lasts - my goldies always went for the roots first, and all that was left was a half dying plant they gobbled down a while later...

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my goldies actually went for the leaves first, leaving the roots hanging out from their mouths like whiskers