49 and 1681 are squares with an even number of digits, where both halves are squares, and no zeroes are used.
List all such numbers below 10^10.

number    sq root  two sq roots

49             7      2   3
1681          41      4   9
225625       475     15  25
2528178961 50281    159 281
3132976729 55973    177 277
8122515625 90125    285 125

There are no more  through 14-digit numbers, through which the program checked.

 For n = 1 To 10000000
   n2$ = LTrim(Str(n * n))
   l = Len(n2)
   If l Mod 2 = 0 And InStr(n2, "0") = 0 Then
     l2 = l / 2
     sq1 = Val(Left(n2, l2))
     sq2 = Val(Mid(n2, l2 + 1))
     sr1 = Int(Sqr(sq1) + 0.5)
     If sr1 * sr1 = sq1 Then
       sr2 = Int(Sqr(sq2) + 0.5)
       If sr2 * sr2 = sq2 Then
         Text1.Text = Text1.Text & n2 & Str(n) & "    " & sr1 & Str(sr2) & crlf
       End If
     End If
   End If
   DoEvents
 Next

Posted by Charlie on 2018-12-05 10:28:31