It turns out that square roots are certainly not alone in having apparently random digit sequences. As an example, the table on the next page gives the digit sequences for some cube roots and fourth roots, as well as for some logarithms and exponentials. And so far as one can tell, almost all these kinds of numbers also have apparently random digit sequences.
In fact, rational numbers turn out to be the only kinds of numbers that have repetitive digit sequences. And at least in square roots, cube roots, and so on, it is known that no nested digit sequences