experimentation is such a repetitive word
The word’s origin is Latin, within the verb experiri.
This verb is made up of two parts: the prefix ex- from the preposition ex (out of, from), denoting thoroughness or achievement in this instance, and the nonattested verb periri, presumably meaning to try, and possibly a cognate of the Greek verb πειράομαι (to try) or περάω (to pass through). Therefore, on a basic level, experiri means 'to try something thoroughly, to test something out repeatedly.' Latin created a noun from this verb, the noun experimentum, combining the verb with the suffix -mentum, meaning 'the result of the action of testing,' or 'the process of testing in itself.'
When experimentum was brought into English, it was first used as a noun, but as often happens with language, possibly to replicate the particular specificity of that noun as an action, the verb ‘to experiment’ was created. The noun 'experimentation' was formed from that verb and the suffix '-ation,' meaning 'the action or process of experimenting.'
Funnily enough, the suffix '-ation' here is playing almost the exact same role as the suffix -mentum does in Latin. So, on a very basic level, 'experimentation' means 'the action of the process of trying something thoroughly,' which is quite repetitive, but perhaps that is fitting for the word itself.
Other fun facts:
experiri shares a root with the Latin words periculum (danger, or where we get the word 'peril'), and porta (gate).
The verb can also mean 'to undergo,' and, through its present active participle experiens, is also the root of the English word 'experience.'
Interestingly, this verb is deponent, i.e. the verb has passive voice forms only but is translated with the active voice. I suspect this is because the idea of testing was similar to how we understand it now: the outcome is out of our control and whatever happens is not something we can necessarily exert agency over; I am not so much doing a test as I am observing the outcome of the test.
~nan
[This word study ambushed me. I think I was figuring out which verb had to be the shared root of 'experiment' and 'experience' and then was yanked deeper into the weeds of language.]