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Do 臭い{くさい} and [腐る]{くさる} have similar roots? They obviously sound very
similar; the only difference in pronunciation is the final mora, but maybe
that's only because of the part of speech. The meanings are related as well.
When things rot, they tend to smell bad. Of course, 臭い isn't restricted to
just bad food, but meanings tend to change/broaden over time.

So I'm wondering, were these once pretty much the same word, separated once
they were given kanji? Or have they always been thought about separately, and
the sound/meaning is just coincidence?
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etymology
Are 臭い{くさい} and 腐る{くさる} related?
[語源由来辞典](http://gogen-allguide.com/ku/kusaru.html) lists theories that they
might be connected for the very same reason you mentioned, among others.

>
> 動植物が腐ると悪臭を発することから「くさあるる（臭荒）」とする説もあるが、「くさい（臭い）」は「くさる」が語源なので、前後関係が逆転している。「くそある（糞生）」から「くさる」に転じたとする説もあるが、「くそ」も「くさる」もしくは「くさい」から生じた語と考えられるため、この説も採れない。

The way I understand it, it is generally believed that 腐る, along with くそ,
stems from 腐る, but that is not proven (and there are other conflicting
theories, such as 腐る stemming from 糞荒【くさあるる】, whose reading I can't quite
explain).

Apart from that, I've been able to retrieve two related citations from the
岩波古語辞典, from two different sources. The first one is for 腐り, from a
[Yahoo!](http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q14144385679)
question.

> 「クサシ(臭し)・クソ(糞)と同根。悪臭を放つようになる意」

The second one is for 臭し (classical form of 臭い), which can be found
[here.](http://www.ctb.ne.jp/~imeirou/soumoku/k/kusunoki.html)

> <クサリ(腐)・クソ(糞)と同根> はげしい、いやなにおいがする。悪臭を放っている。

As you can see, both entries cross-reference each other.

So, it seems like the 腐る・臭い connection is definitely the most agreed upon
theory, although there does not seem to be a definite proof. There definitely
seems to be some kind of connection between (at least two of) くそ, くさい and くさる,
though, although we can't know for sure how exactly it's laid out.
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