Do I need an apostrophe in "These trees’ roots"?
"Wow!!! These trees' roots are so long!"
In this example the speaker can see both roots and the trees themselves.
Yes, you need the apostrophe.
-s' denotes possession of some thing or things by multiple owners. The roots belong to the trees; the trees own the roots. Therefore, the roots are the trees' roots.
Yes, you need the apostrophe, and you need it right where it is: make sure that the apostrophe is after the "s", not before.
-s' is the possessive ending for plural nouns (e.g. trees becomes trees'), while -'s is the possessive ending for singular nouns (e.g. tree becomes tree's).
Hence, The roots of these trees becomes These trees' roots.
And The roots of this tree becomes This tree's roots.