Specifically carrots and next to that the roots of all plants and trees, you can only know from context whether carrots or plant roots are meant. And square root is wortel as well, but there won't be many contexts where this can be mixed up with the food or plant root meaning. :) And it's used methaforically as well: Mijn wortels liggen in Utrecht = My roots are in Utrecht.
- radish = radijs
- beet = biet (e.g. rode biet and suikerbiet)
- cassava = cassave / broodwortel / maniok
- ginger = gember
Both plurals are grammatically correct, but which one you actually use depends on the context:
∆ When referring to the vegetable or the roots of something (such as a square root), only wortels is correct.
∆ When referring to the origin of something, only wortels is used.
∆ When referring to the vegetable or the roots of a plant, both wortels and wortelen are fine.
∆ When referring to the cause of something, again, both wortels and wortelen are correct.
Hope this helps!