Yes, BIRTHROOT is a Scrabble word!

Letter values in Scrabble US: B 3, I 1, R 1, T 1, H 4, R 1, O 1, O 1, T 1.

Is it a valid word?

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

trillium of eastern North America having malodorous pink to purple flowers and an astringent root used in folk medicine especially to ease childbirth

Also: purple trillium, red trillium, trillium erectum.