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To make it easier to remove weeds with long roots, water the soil around the weed thoroughly. Completely soak the weed.
Then, insert your trowel vertically into the soil as close as possible to the weed stem. You should then be able to pull the weed out, roots and all.
Another option is to simply spray the weed with a weed killing chemical. Just be certain to not let any over spray land on any surrounding plants or vegetables.