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Trace idea that is wrong and root it out (9)

Ross

I believe the answer is:

eradicate

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'out' is the definition.
Although both the answer and definition are verbs in their base form, I cannot see how they can define each other.

'trace idea that is wrong and root it' is the wordplay.
'trace idea' can be anagrammed to 'ERADICATE'.
However, I'm not clear how this is indicated.

Can you help me to learn more?

(Other definitions for eradicate that I've seen before include "Dispose of" , "Get rid of, eliminate entirely" , "Completely remove" , "carry out a purge" , "Kill" .)

I've seen this clue in The Globe and Mail.
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