Q:

Number in Number-squared

Consider a sequence of natural numbers for which N appears as a substring in N^2. A018834
Output the nth element of this sequence.
Rules
Program takes only n as input and outputs just one number - N.
The sequence can be 0-indexed or 1-indexed.
Sequence: 1 5 6 10 25 50 60 76 100 250 376 500 600 625 760 ...
Squares:  1 25 36 100 625 2500 3600 5776 10000 62500 141376 250000 360000 390625 577600 ...

This is code-golf so shortest code wins.

A:

Perl 6, 33 31 bytes
-2 bytes thanks to nwellnhof
{(grep {$^a²~~/$a/},1..*)[$_]}

Try it online!
Explanation:
{                            }  # Anonymous code block that returns
 (                      )[$_]   # The nth index of
  grep {          },1..*        # Filtering from the natural numbers
        $^a²                    # If the square of the number
            ~~/$a/              # Contains the number

A:

05AB1E, 6 bytes
1-indexed
µNNnNå

Try it online!
Explanation
µ         # loop over increasing N until counter equals input
 N        # push N (for the output)
  Nn      # push N^2
    N     # push N
     å    # push N in N^2
          # if true, increase counter

A:

JavaScript (ES6), 43 bytes
f=(n,k=0)=>n?f(n-!!(++k*k+'').match(k),k):k

Try it online!

Non-recursive version, 47 bytes
n=>eval("for(k=0;n-=!!(++k*k+'').match(k););k")

Try it online!

