The decimal representation of sqrt(2) is
sqrt(2) = 1.414213562.............................…
The sequence of digits do not repeat but is still infinite.
Just one more thing before I sign off. If you enter 1/3 on the calculator you will get the result
1/3 = 0.33333333..........
here the single digit 3 repeats ad infinitum. To show that this is indeed the case, let
x = 0.33333333...............
Then on multiplying both sides by 10, we get
10x = 3.33333333..........
Subtracting both sides of the first equation from the second:
10x - x = (3.33333333..........) - (0.33333333..........)
9x = 3
x = 3/9 = 1/3
Voila! No trickery. This is how it works.