My hemoglobin is 10.8( range 12-16.5)(female,25.) do not experience any symptoms.it was a routine test. how low is this?can i manage without medicine?

Find the cause: Anemia has over a hundred different causes. If it's iron deficiency, the cause must be sought -- you don't want to miss bleeding from a cancer or bad stomach ulcer. It may simply be your monthly loss and/or your diet (if you're a non-supplementing vegetarian, expect health issues.) Other anemias warn of serious treatable disease. Let the workup proceed. Best wishes.