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The phrase "am irrational" is correct and usable in written English.
It can be used when expressing a state of being or a personal admission of irrationality.
Example: "In moments of stress, I often feel that I am irrational in my decision-making."
Alternatives: "I act irrationally" or "I can be unreasonable."
Dictionary
am irrational
noun
A real number that can not be expressed as the quotient of two integers, an irrational number.
synonyms
Exact(2)
"I am irrational.
I find her to be too rigid and controlled, a bit of a snob and a health obsessive, while I'm sure she thinks that I am irrational and over-emotional, and too dependent on others.
Similar(58)
It's irrational".
It is irrational".
It was irrational.
It was irrational, he knew.
Yeah, it's irrational.
Is Putin being irrational?
This may be irrational.
Children are irrational.
Fear is irrational".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com