Is prove a word in the Scrabble Dictionary

Yes, prove is playable

...and is worth 12 points.

Found in the following dictionaries

Enable (Words with friends)
SOWPODS (Collins Scrabble Words)
OTCWL2014 (NASPA Word List 2014)
TWL06 (NASPA List 2006)

"Prove" Definition

verb-transitive

Archaic To find out or learn (something) through experience.
Law To establish the authenticity of (a will).
Mathematics To demonstrate the validity of (a hypothesis or proposition).
Mathematics To verify (the result of a calculation).
Printing To make a sample impression of (type).

phrasal-verb

Prove out To turn out well; succeed.

verb-intransitive

To be shown to be such; turn out: a theory that proved impractical in practice.

verb

To show (oneself) to be worthy or capable .
To turn out especially after trial or test .
To check the correctness of (as an arithmetic result).
To establish the existence, truth, or validity of (as by evidence or logic) .
To demonstrate as having a particular quality or worth .