When I was a child we all made ginger beer, and ginger beer plants. They ALL worked. They did not include grated ginger. I can even remember the recipe by heart.
A ginger beer plant is 1 teaspoon compressed yeast (the sort that comes in a cake form from the fridge of a health food shop) 1 teaspoon ground ginger (from the supermarket) and 1 teaspoon of sugar in 2 cups of water - add the water slowly so that you have a slurry with no lumps. Put it in a jar (without a lid) somewhere in the kitchen. Add 1 teaspoon ginger and 1 teaspoon sugar each day for 7 days.
Heat 8 cups sugar and 48 cups of water until the sugar has dissolved. Add 1 cup lemon juice. Strain the ginger beer plant through muslin and add the liquid from it to the ginger beer. Bottle the ginger beer. Divide the muck in the muslin into 2 new ginger beer plants, add 1 pint of water to each, and start again. Start drinking after 1 week.
Probably better to make half a plant and half the recipe. After a while you get sick of it, forget to feed the plant every day, and your mother chucks it out. Then a month or so later, you start your next plant. I can't remember what I did with the second plant each time - it was probably chucked out too, as every kid knew how to make ginger beer, and could create their own plant when they wanted to. It was about the first bit of cooking you were allowed to do.
We used washed out beer bottles and crown seals. Occasionally some enterprising child left their bottles in the sun (they wanted it to be ready faster) or forgot about the ginger beer and the bottles burst. This is especially likely to happen if you leave your bottles along the window ledges in your sun room on the hottest day of the year.
We also sometimes made lemonade with a similar recipe. It was much better as it didn't need a plant, and was ready to drink in 2 days (two weeks from start to actually being able to drink ginger beer was forever). However, lemonade was much more likely to explode.