How do you clean cheesecloth full of bean roots? Related: How do you clean cheesecloth?

My problem is a bit more complex. I sprout beans in cheesecloth and it's been working okay. The cheesecloth is able to get some of the bean roots off the beans when I harvest the bean sprouts so that I don't have to eat a lot of roots. The drawback: I end up with a piece of cheesecloth full of bean roots. Handwashing it helps remove some but not all the roots. Better ideas?
You clean it by throwing it away. Is it worth the trouble?