While many people love to cite the word "antidisestablishmentarianism" as the longest word, a quick google search will tell you this isn't the case. Merriam-Webster will not even list it as a word because it is not acutally in usage, it is only used as an example of a long word. The fun of this word, as one commenter said, is finding all the different prefixes and suffixes. While many would say the the base word is "establish", an astute tutor would know that "establish" is a stem word and that there are more prefixes and suffixes that can be peeled off. A better answer in regard to what the base word is would be "stable", but even this is not the complete answer. There is the prefix "e-" and the suffixes "able" and "ish" in "establish". That leaves a bound base element of "st". This comes from the Latin root stabilis meaning "to stand, make or be firm". When you establish something, or make it stable, it is firmly in place. The "st" in related words shows this meaning.
Vestiges of this Latin Root can be seen in so many words that share a similar connotation of "making a stand" or "being firm" as in the words stand, stance, stare, state, station, statue, constant, and rest.
The word sum for "establish" would look like this: e + st + able/ + ish--> establish. The slash after the 'e' in the "able" suffix shows that the 'e' is replaced by the vowel suffix. Knowing this suffixing rule is so important for spelling and reading. This spelling/orthography tool is used in Structured Word Inquiry. This method dives deeply into words and helps students become better spellers than when told you just have to sound it out or memorize it.