"obvious realization" is correct and usable in written English
You can use it to describe a moment when something becomes clear or apparent to someone. For example, "She had an obvious realization that she had made a mistake".
With Gruden, the first and most obvious realization was how ignorant I was.
He says about his relationship with his other girlfriend, Isabel: My Spanish was getting better, despite myself, and I experienced, with the force of revelation, an obvious realization: our relationship largely depended upon my never becoming fluent, on my having an excuse to speak in enigmatic fragments or koans..
In a 2001 ruling, the Department of the Interior v. Klamath Water Users Protective Association, the Supreme Court said that "the deliberative process privilege rests on the obvious realization that officials will not communicate candidly among themselves if each remark is a potential item of discovery and front page news".
He says about his relationship with his other girlfriend, Isabel: My Spanish was getting better, despite myself, and I experienced, with the force of revelation, an obvious realization: our relationship largely depended upon my never becoming fluent, on my having an excuse to speak in enigmatic fragments or koans...
The most obvious realization that comes after a few days at the wheel of the 350Z is that it could stand even more horsepower.
When I got up the courage to turn around and look down to face what I still hoped was just someone's belongings, my stomach dropped at my obvious realization.
This realization, obvious in retrospect, led to the widespread acceptance of the South African australopithecines as human ancestors, and the important corollary that bipedalism preceded other distinctive human attributes (Gundling 2005).
Even more obvious was his realization that they're not so different, the yogis and him.
This realization — as obvious as it is worrying — has recently stirred the beginnings of a response from researchers, architects and, not least, parents.
And at this point, the uncharitable reader might well observe that it took the egocentric narrator nearly 300 pages to arrive at a fairly banal realization that seemed obvious enough more than 200 pages earlier, when he acknowledged, "I had never thought rightly of how to be a parent or a husband, only of possessing a child, of owning a wife".
It is obvious that if a SCRS realization A of a real n-tuple (Lambda =(lambda_{1},ldots,lambda_{n})) has CRS λ, then (lambda =lambda_{k}) for some (kin{1,2,ldots,n}).
