#Jelly, 8 7 bytes

1 byte thanks to @Sp3000.

DSƲðÐf

Test suite.

###Explanation

DSƲðÐf  Main monadic chain. Argument: z

     Ðf  Filter for truthiness:
D            convert to base 10
 S           sum
  Ʋ         is perfect square

Jelly, 8 7 bytes

1 byte thanks to @Sp3000.

DSƲðÐf

Test suite.

Explanation

DSƲðÐf  Main monadic chain. Argument: z

     Ðf  Filter for truthiness:
D            convert to base 10
 S           sum
  Ʋ         is perfect square

#Jelly, 8 7 bytes

1 byte thanks to @Sp3000.

DSƲðÐf

Test suite.

###Explanation

DSƲðÐf  Main monadic chain. Argument: z

     Ðf  Filter for truthiness:
D            convert to base 10
 S           sum
  Ʋ         is perfect square

#Jelly, 8 7 bytes

1 byte thanks to @Sp3000.

DSƲðÐf

Test suite.

###Explanation

DSƲðÐf  Main monadic chain. Argument: z

     Ðf  Filter for truthiness:
D            convert to base 10
 S           sum
  Ʋ         is perfect square

#Jelly, 8 bytes

b⁵SƲðÐf

Test suite.

###Explanation

b⁵SƲðÐf  Main monadic chain. Argument: z

      Ðf  Filter for truthiness:
b⁵            convert to base 10
  S           sum
   Ʋ         is perfect square

#Jelly, 8 7 bytes

1 byte thanks to @Sp3000.

DSƲðÐf

Test suite.

###Explanation

DSƲðÐf  Main monadic chain. Argument: z

     Ðf  Filter for truthiness:
D            convert to base 10
 S           sum
  Ʋ         is perfect square