Why learning by roots works
Research (find Baleghizadeh, S., & Yousefpoori Naeim, M. (2011), "Promoting Vocabulary Retention through Etymology Presentation," Journal of Theory and Practice in Education.) shows that you don't even need to have a related word for an etymology-based learning system to work- though that is a cherry on top. In the study, Iranians learning English vocabulary needed to learn a vocabulary list of 30 words. Like you, they were encountering a language in a new alphabet, where it gets even harder to distinguish something as simple as stall versus small.
Unlike you- this study was actually on 'hard mode' because the method wasn't even trying to show the cognates between Iranian and English- it just discussed the etymology of the English word itself. One group of students learned the words the usual way- the other did this seemingly difficult extra work of learning the lore behind the English word.
The students were then tested two months later and the ones doing things 'the usual' barely absorbed any of the wordlist- this may sound familiar. Weeks and weeks of grinding without a method, and only a few new ones stuck.
The ones who had learnt the word alongside reading about its etymology memorized a much larger amount of the new words, and they stuck in long-term memory. The extra work more than made up for itself- because even if the ONLY thing tested was the output that mattered- it still won.
What's amazing is that the extra information didn't make things harder- it made it easier. The mere act of meaningfully wrestling with the new word is where most of the benefit comes from. That's the first thing- reading a page of "lore" or backstory- that is, the etymology- of a root seems like extra information but it's so effective, it's worth the time.
Inventing a mnemonic device is next.
Early on in my Ukrainian learning, I would come up with a silly mnemonic device (a common method for many people) to memorize a word. Like, I memorized that to літати (litaty) to fly was to feel light and feathery. If you're lighter than air, you can літати (litaty).
What's funny is that I discovered that many of my mnemonic devices to associate a Ukrainian word with an English idea were accidentally using cognates anyway. As an etymology enthusiast I asked myself, why not lean into it and make as many of your mnemonics as possible out of REAL, actual links?
A second thing, I was getting these Ukrainian near-synonyms like залітати (zalitaty), пролітати (prolitaty). The prefixes threw me for a loop and it was very difficult to come up with meaningful tricks for them. I soon realized that I could only afford to come up with memory tricks for what seemed to be the base of the word, and couldn't come up with a new one for all these variations.
I did start to realize, though, that Ukrainian prefixes had their own logic. It was enough to learn the root- the base- and to learn the basic mechanics of the dozen or so prefixes.
What my book does is put this all together. First, no matter what your native language is and whether it has a cognate for every root (it won't,) the mere act of wrestling with it, engaging with new information, will help you sear the root into your long term memory, just like it worked for the Iranian students learning English. What seems like a bit of extra work up front will be the main reason you will still know your new vocabulary words in months, when you're put to the test later.
Second, there's a good chance the book will point out a relation you may have not noticed before. As mentioned, diving into Ukrainian etymology kept revealing connections I hadn't noticed yet. Even better than the Iranian study- not only are you meaningfully interacting with the root- there's even scaffolding to hold on to.
Examples like when you learn that прям- (priam-) straight ahead is related to Romance prime, the first thing in front of you (and actually related to native Germanic English first, as well). Or that брати (braty) is related to English bear, like to bear good news, and Latin-origin infer, defer or Spanish inferir, diferir.
Learning Slavic languages will never be quite full of the freebies you get with Spanish or German.
You can't just go off ordering Bier or asking for Kaffee MIT Milch, or getting Butter on your Brot. But I can tell you that the root пи- (py-) drink that underlies пиво (pyvo), пити (pyty), is actually descended from the very same Indo-European word that birthed Latin-origin words like potion, imbibe, or Spanish beber. A напій (napii) as something you "drink up" is something like what you imbibe, a potion to пити (pyty), from Latin in-bibere, also from this same Indo-European. You'll see how Ukrainian uses prefixes like на- (na-) and ви- (vy-) and others to extend the meanings of roots, but most importantly you'll never see a пи- (py-) word again and doubt the general meaning of it.
Similarly, don't expect Romance loanwords to save the day every time like when you learnt Spanish or French. Unlike the French word Renaissance (that a native French speaker transparently understands as "the re-birth," like the re-nativity) you will see the word відродження (vidrodzhennia). You'll learn what род- (rod-) really means- where it comes from- and when you find it in НАродження (NArodzhennia), ЗАродження (ZArodzhennia), etc, you'll have an idea what's going on.
Another high level concept, просвітництво (prosvitnytstvo) Enlightenment will make sense when you understand that it's from when "the light" світ (svit) came through (prefix про- (pro-)). You'll learn the root світ- (svit-) for light, the (over)world and have no trouble with освіта (osvita) (education) coming from being enlightened from all around you, or світлення (svitlennia) lighting or світанок (svitanok) dawn.
You'll enthusiastically take on саморозвиток (samorozvytok), from ви- (vy-) to wind, becoming розви- (rozvy-) to unwind, de-velop, given the other root сам- (sam-) meaning alone, on your own, by your self. When you see other само- (samo-) prefix words you won't be at a loss. And other words with ви- (vy-).
The goal by the way, just as a reminder, is not that you memorize every single one of the 8000+ words I included. The goal is to have an intuitive grasp of the basic meanings of the roots. This is not some type of linear coursebook that fails if you do it in just the wrong order or skip a week, a month, or even a year. Language learning takes work so I'm not telling you to take breaks. But this book is not sensitive to failure from those breaks. And it's a reference that stays useful from nearly your A0 true beginners beginning to your C2 plus polishing of subtle synonyms.
That's the difference. Well, just one of them.