Is there any kind of known pattern to $\sqrt 2$ in base 2? Is there any classification categories for decimal digits of numbers that for example would put $\sqrt 2, \sqrt 3 \cdots \sqrt n$ into separate category than $\sqrt 2, \sqrt 3 \cdots \sqrt n$
Or given a decimal expansion with arbitrary precision, or definition of digit in the nth place (not necessarily decimal expansion) to get a probability of which class of numbers the number is likely to be? e.g. transcedental or algebraic of degree k?