How Big will the roots get in Hydroponic?

Hello I am new to growing and I have a question how big will the roots get in Hydro system and how much space will they need, they will grow in a box 4ft x3ft x6in and there will be 18 of them in 1 box for vegging and 9 in a box for flowering, is it enough space? Also is it problematic to transfer them from 1 box to another, will it damage the roots , if it will would it be a bad problem or just a lil shock?

Thaks for replies, (sorry for my English this is my 2nd language)