I think that might be chanzo/vyanzo: beginning, origin, source, root, cause.
I find this dictionary useful:
(It's a cluttered interface, but you can type any word, English or Swahili, into the search box then scroll down for the definition, conjugations, and sometimes good example phrases. There is also a useful Swahili noun class mini-reference at the bottom of every page.)
I wouldn't rely on Duolingo's accepted answers as gospel. (They also suggested "its drawing" for mchoro wake, despite the fact that it would be unusual - but not impossible - to find an "it" that can draw. - Nice example in that discussion: https://www.duolingo.com/comment/22708145.)
However, Swahili translations of the Bible use "mzizi" (root) as well as "shina" (roots and stem of a tree) metaphorically, as in "the root of all evil".
(Google: 'mzizi translated as metaphor in Swahili Bibles'.)
We are also thinking metaphorically when we talk of a family tree, so I suppose Swahili might use the roots metaphor in that context too.
I will grant that a Swahili translation of the Bible probably underwent a bit more copy editing than Duolingo translations.
However, those translating the Bible into Swahili would presumably also be highly proficient in English (if Western missionaries, it well might have been their only native language). Even if "mizizi" isn't really naturally used with any figurative meaning in Swahili, it could still wind up in a Bible translation simply because the corresponding English figurative use is so longstanding (i.e. dating back 800+ years) and hence natural to the translators, but not inherently to the language they're translating into.
Yes, definitely a more thorough translation. Those missionaries spent lifetimes learning the local language and culture so that the Bible would make sense in translation. If you google 'mzizi translated as metaphor in Swahili Bibles' you come to a page in a whole book about the translation of biblical metaphors in Hausa and Swahili.
I imagine metaphors about plant growth would be recognizable to the Swahili communities at the time.
As vtopphol points out, it worked for the Aramaic/Hebrew/Greek to English translations.
My conclusion is that it would be safe to use "mizizi" metaphorically. But maybe a native speaker will be able to clarify that.
What's an M/MI noun doing in the N/N skill? I went for "its root" because I thought "yake" indicated a singular noun (which it would for an actual N/N noun), but of course this is in fact a M/MI noun, so I should indeed have said "Its roots". But it would be good if skills for particular noun classes could primarily have nouns in those classes so we can focus better on learning their forms.
Yes, "yake" could mean its, his or her, but in this case we're talking about the roots of a plant, so "its roots" is the most logical translation.
You might use "his/her roots" when talking about someone returning to their original home or family, "going back to his/her roots", but I think the Swahili word mizizi just means the roots of a plant and not the other kind of roots.
If mizizi can include edible roots, perhaps "his/her roots" could work in that context. Otherwise, as I said above, "its roots" is the most logical translation here.