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Is it halal to drink something that has ‘fermented ginger root extract’ as one of its ingredients?

In the west there are many soft drinks that include this ingredient.

All kinds of alcohol are Tahir (ritually pure), however are not permissible to drink, except for wine which is also Najis, and Beer (Maa al-Sha'eir) which is also Najis (ritually impure) as an obligatory precaution.
Therefore, the medicines and the perfumes containing alcohol are pure and can be used.
As regards to consumption, it is permissible to comsume such food if the amount of alcohol is very minute, e.g., 2%, except for wine.