3. There is absolutely no evidence to _____ that this is a viable option.suggestrequirerequesthint

The appropriate word to fill in the blank is "suggest."

Detailed Explanation

1. Context of the Sentence: The phrase "There is absolutely no evidence to _____ that this is a viable option" implies that something related to supporting the claim of viability is missing. The word that fits best here is one that indicates offering support or indication rather than asking for something or needing something.

2. Analysis of Options:

   • Suggest: This word means to put forward an idea or plan for others to consider. It fits perfectly in the context of lacking evidence for an option being viable.
   • Require: This term means to need something, which doesn’t fit the context of the sentence.
   • Request: This means to ask for something, which does not align with the idea of providing evidence.
   • Hint: This means to suggest something indirectly, which also does not match the context as directly as "suggest."

Conclusion

Thus, the completed sentence reads: "There is absolutely no evidence to suggest that this is a viable option."