Responding to the interesting square root question, Egyptian fraction arithmetic was based on positive rational numbers scaled to concise unit fraction series. Irrational and higher order numbers like pi were approximated bu scribes. Pi. for example, was approximated two ways, 256/81 and 22/7, each for special purposes.
Irrational numbers like the square root of 2 would have been approximated by the Babylonian method (that I learned as a high school freshman algebras class).
does a poor job in intellectualizing the simple aspects of the method as I learned. In addition, I suspect Wikipedia;s data also offers unclear historical aspects of the method that Egyptian scribes used to create approximate unit fraction series.
When second degree algebra equations were solved by a Berlin Papyrus