Yes, EXAMINE is a Scrabble word!

Letter values in Scrabble US: E 1, X 8, A 1, M 3, I 1, N 1, E 1.

Is it a valid word?

EXAMINE is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

consider in detail and subject to an analysis in order to discover essential features or meaning
observe, check out, and look over carefully or inspect
question or examine thoroughly and closely
question closely
put to the test, as for its quality, or give experimental use to

Also: try out.