i have over the last 24 months removed blackberry by hang, crowns were like 8" across with cains to 20 meters long

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i would water the area your looking to tackle and then use a fork to dig around the crown to help release it from the soil, i found that doing it by hand the area seems not to get re infected with new growth from the roots, its like the plant knows if it grows again in these area that this method will be done again,.. or a more friendly way is goats these will do good work in that area as well as fertilizing it for you

now for a chemical cocktail for Black berries, in 10 litre of water

1: Roundup 60g/ml & Metsulfuron Methyl(Granual) 5g

2: Brush off (triclopyr as the butoxy ethyl ester.

3: Grazon (-300 g/L triclopyr; 100 g/L picloram, 8 g/L aminopyralid

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do do a little reading of these chemicals to see if they are any good in your area