Before he creates Eve, God tells Adam that if he eats any apple from the tree of knowledge, he will die.
You may surely eat of every tree of the garden, but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.
So, the first question is, did Adam relay this information onto Eve? Eve answers this at the beginning of "The Fall" section, when she tells the serpent,
We may eat of the fruit of the trees in the garden, but God said, "You shall not eat of the fruit of the tree that is in the midst of the garden, neither shall you touch it, lest you die."
The serpent then persuades her to go against God by saying that eating from the tree will open her eyes to the world, and, like God, she will know good and evil. At this point, one could argue that her decision would have been rational if she made it based it on the serpent's suggestion that God was preventing her and Adam from evolving beyond who they were at that moment. The fact is, however, that good and evil would have probably been a difficult, if not impossible, concept for her to grasp at that point in her existence. As the Bible states, she made her decision based on how delicious the apples looked and how much more powerful she thought she would become.
So when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate.
Overall, her decision is irrational because she eats the apple without truly understanding the consequences of doing so. The only thing that she knows for sure is that it will in some way change her (up to that point) pleasant life.