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Now that my roots are f'cking huge, i'm noticing some broken off roots floating around, and I guess it is not very good idea to leave them roting like that. Is there any standard cheap way of geting rid of those kind of floaters?

you can use an enzyme to break them down... if it's 5g, get another bucket, lift lid and plant, and place it in a new bucket, clean the old, repeat as necessary (might need help if it's huge).

I use hygrozyme.

I didn't use it the first part of my current grow (ran out) and the water was full of root bits, so I bought more

I'm brewing heisenbergs microbe tea. They should work as an enzyme breaking them down, but I was thinking perhaps there was some easy mechanical way I haven't thought of.

I do what catofcuriosity suggested. I have 6 DWC buckets and use a spare 7th when I do my weekly water changes. I disconnect the air stone and clean each bucket out individually to remove any salts and root bits. I just lift the bucket lid and place it in the 7th to hold it for a few minutes until I am done.

This is my first DWC and I am just running Lucas with a little bit of h202 and a splash of superthrive. So far so good (really good!) and they'll go into 12/12 after my Sunday water change.