Evening,

I am trying to isolate the whole numbers/integers from a pair of numbers within a range. This is the function I am currently using:

Table[{Sqrt[1 + 5 k^2], Sqrt[k^2]}, {k, 0, 500}]

I want to find out which of the Sqrt(1+5k^2) is a square number itself, so a whole number. I am currently having to try a range and read through all my results. What I would like to to use a command, or a different command to the above, to just show those results that give me whole numbers.

I hope I have explained that well enough and am asking in the right place. Thank you in advance.