What word is the root of the most element names?
What does it mean?
Which elements?

Most of the oldest names come from Greek, through Latin. Is that what you mean?
But the later ones seem to have a Latinized ending ( e.g. ium ) tacked onto another root word.

I'm looking for a single word that is the root of multiple element names. Although -um is found at the end of most metals, that is not what I'm looking for.

Try this one on!

My answer: "un", meaning one.

"un" forms the root of a total of four discovered elements:
111: Unununium
112: Ununbium
114: Ununquadium
116: Ununhexium

"un" also forms the root of a reportedly discovered element, #118 (Ununoctium) but the discovery was retracted by Berkely scientists after they could not reproduce results.

Presumably "un" will form the root of three more postulated but undiscovered elements:
113: Ununtrium
115: Ununpentium
117: Ununseptium

LOL .... I don't know if this is what you were asking for, just a fun word play from the first periodic table I could dig up!

http://www.webelements.com/

It will also be in the temporary name for element 119 when that created.

Interesting, but not what I was looking for (because those are only temporary names and will be replaced relatively soon).

Here's a hint - the root that I am looking for is also in 4 elements.

I'll guess the root is Ytterby, a village in Sweden. From this village comes these four elements:
Erbium
Yttrium
Ytterbium
Terbium

You got it, Jelp.