Chinese radicals are components of characters that are made up of more than one part. But in fact some Chinese radicals itself is a single character .For example,the character 辛 can be a chinese radical for characters like 辣. Generally we think 辛 has no radicals,but it's nice to help remember the character as 立+十. Hope this could help you understand better

不是不可拆分，而是不可"過分"拆分 We can break "inside" down into "in + side", but we will not go on to break it down , like to get"i + n + si + de" or what. although we have a "lie" in "believe", it doesn't mean we should break and get "be + lie +ve"

Chinese radicals are indivisble by semantic meaning; not by stroke shapes. What you see are now the abstract form of seal characters. For example, dragon, 龍 is a radical. You cannot break it down into 立 or 月. 風 is another complicated radical which does not have 虫 as a simpler component. BTW, the traditional form shows the insect radical is because ancient Chinese believe that wind is caused by the beating of insect wings!

In my opinion, Chinese radicals are indivisible. It's only for memorization to further divide a radical, and you are not necessary to remember this method. I don't think it makes sense to apart a word in that way.