There's no direct translations for "eradicate." However, dragons like to destroy things so you have a lot of close words to choose from. Here are a few to consider. It's hard to know what will fit best without a sentence for context, but any of these could work:

• al 'to destroy'
• evenaar 'to extinguish'
• krii 'to kill'
• kriin 'to slay'
• qahnaar 'to vanquish'

The dictionary entries linked above will give you usage examples and any special connotations those words may have.