No, I don't believe you are correct: a calculator can represent sqrt(2) as sqrt(2), just the same as we can on paper (perhaps you are calling this an algebraic

No, I don't believe you are correct: a calculator can represent sqrt(2) as sqrt(2), just the same as we can on paper (perhaps you are calling this an algebraic representation). In fact, I'm confident that Casio - probably the market leader in scientific calculators - is doing exactly this, storing the exact number. Casio does not appear to approximate simple surds as floats until it becomes necessary, and stores the exact number sqrt(2), just as it stores exact representations of rational numbers wherever reasonable (and, it correctly distinguishes whether it knows a number exactly or only as a float - it refuses to convert inexact floats into fractions, but will convert exact numbers). Calculator phone apps don't compete at this level - which is surprising, I would have thought smartphones would have put calculators against the wall.