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It seems plausible to me, and I would like to know how to verify it.

Why I think xahesh might be cognate with question:

xahesh (IPA: /xɑːheʃ/) in Modern Persian is a noun meaning "request, plea". The root xah- is from the verb xastan /xɑːstæn/ meaning 'to want, desire'. It is spelled xwahesh, and was pronounced /xwɑːhesh/, as it still is in some dialects like Dari. The suffix -esh is from Middle Persian -eshn (/eʃn/) (or maybe -ashn) , which has essentially the same function as Latin -tio, tionis, turning a verb into a noun, though I'm not sure if these two are related.

Several words in Persian beginning with xw- appear to be derived from PIE roots beginning with *sw. For instance xwab (/xɑːb/, formerly /xwɑːb/) "sleep" is listed in some etymology dictionaries as a derivative of PIE *swep, cognate with Greek ὕπνος, and Latin somnus. Another example is xwahar (/xɑːhæɾ/ or /xwɑːhæɾ/) "sister", is clearly from PIE *swésōr, cognate to sister, Schwester, soror, etc. This does not appear to be a strict rule however, since for instance xwandan (/xɑːndæn/, /xwɑːndæn/) "to read, sing", is supposedly cognate with Latin canō, canere, from PIE *kan, which is not labialized.

Given that Latin quaero is rhotacized quaeso, which resembles the h/s counterpart of xwah-, and has a similar sense to it, I think it's reasonable to guess that the two may be cognates, but I've not been able to find this written down anywhere.

Now, this is almost certainly because I don't know where to look. I'd appreciate a response pointing out what is the right academic source or procedure for verifying such guesses. For instance, are there standard academic references for looking up the PIE roots of Persian/Iranian words?

A-K
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    Cheung 2007 http://dictionaries.brillonline.com/search and perhaps Mayrhofer 1986-2001 Etymologisches Wörterbuch des Altindoarischen – Alex B. Apr 27 '15 at 02:53
  • Definitely the origin of the word question started not from PIE s- but from PIE k^w- – Anixx Apr 27 '15 at 03:42
  • It seems somewhat possible at first glance. According to Wikipedia, Iranian did have a sound change k > x in some conditions, and also a sound change s > h. I'm not sure why the /w/ would be there, though, because Iranian is supposed to have lost the labialization of the PIE labialized velars. – brass tacks Apr 27 '15 at 04:02
  • @Anixx: That's right. The kwo words don't have a consistent fate in Persian though. For instance there's ki /kiː/ meaning "who", and chand /tʃænd/ meaning 'how much/how many'. Possibly they both have the same PIE root kwo as quaerere. It seems plausible to me that some of these kw- words end up as xw-. – A-K Apr 27 '15 at 04:03
  • @sumelic: That's also puzzling to me, since the common xw- I mentioned is indeed a labialized phoneme (couldn't type a superscript here), and words like xwahar look to have retained that original labialization, despite what is supposed to have happened. – A-K Apr 27 '15 at 04:07
  • I think finding out the source of the /w/ sound should make things clearer. Perhaps an excrescent /w/ developed before some vowels at some point in the history of Persian. I will try to do more research. – brass tacks Apr 27 '15 at 04:08
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    Words like "ki" and "chand" apparently don't have the same root as "question", by the way (but "xahesh" might). "Ki" and "chand" clearly descend from the PIE interrogative or relative pronoun, *kʷis (cognates in Latin, qui and quam). However, the word "question", despite it's apparent similarity in meaning, is not considered to derive from this root in any etymology I can find. – brass tacks Apr 27 '15 at 04:24
  • @sumelic how do u put superscript here? – Anixx Apr 27 '15 at 06:17
  • @Anixx: Oh, I just copied and pasted that word from Wiktionary. The superscript w in it is the distinct Unicode codepoint rather than a variant of lowercase w. I don't know if we have any real superscript codes that can be used in comments. – brass tacks Apr 27 '15 at 06:34
  • Here is a potential answer: the Persian xwahesh from PIE sweh₂d-u- "sweet", through Avestan xʷāsta* "?", cognate with Sanskrit svādu "tasteful", which would make it related to persuade in English, and not question. This is stated as fact in a book of Persian/PIE roots by Ali Nourai, but I'm not sure how trustworthy it is, and I can't find an Avestan dictionary online at the moment to look up xʷāsta. – A-K Apr 27 '15 at 08:52
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    @A-K. Avestan xʷāsta- and Skt. svādu- are correct, but *sweh₂d-u- does not account for the Sogdian and Bactrian and Armenian forms with /z/ (see my answer). – fdb Apr 27 '15 at 13:17
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    And to your other question: IE k and kw become Indo-Iranian k before IE back vowels, but č before IE front vowels. This explains the difference between ki and čand. – fdb Apr 27 '15 at 13:23
  • ....from Iranian ka- and či-want- respectively. – fdb Apr 27 '15 at 13:33

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Henning, Das Verbum des Mittelpersischen der Turfanfragmente (1933) p. 187 posited Iranian *xwaz, ‘wish, want’, represented by Middle and New Persian xwāh-, with long-grade present stem, the regular SW Iranian shift of /z/ to /d/, and then a specifically Persian dialect shift of /d/ to /h/.

Johnny Cheung, Etymological dictionary of the Iranian verb (2007), pp. 459-460 similarly posits Iranian *xṷaz, represented also by Sogdian xw(ʼ)z, Bactrian χωζ- and others, also the Armenian loanword xuzem. No non-Iranian cognates are known.

The etymology of Latin quaero, quaestio etc. is debated, but none of the proposed suggestions links up with the cited Iranian root.

fdb
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I am not sure about this , but persian word khast written as khwast , sounds similar to english word quest with exact same meaning... in middle persian (pahlavi) it is : xvāst] xāst

mercuryabz
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    Similarities in two (not closely related) modern languages are not very useful, unfortunately. Sometimes they indicate that the word has been borrowed one way or the other (eg Telephone in many languages); sometimes they are coincidence. For them to be related would require that the words have gone through the same series of sound changes (or of not changing) in both languages. This is unusual, and if it has happened, then there will be many words showing the same correspondences. – Colin Fine Nov 17 '19 at 13:50