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Settings>Safari>Clear Searches.

TEG

I don't see that in the settings.

What works for me is to go to Settings>Safari>Search Engine, change to whatever the other search engine is. (I use google so I switch it to yahoo)

Then I tap Clear History and switch the Search Engine back to google
 
just tried that and all the search suggestions are there. I'm worried someone playing with my phone will stumble upon these searches.
 
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