crystal, 38 bytes

Result

WA

Code [DL]

loop{p (1+8*gets.to_i 2)**0.5%1>0?0:1}

stdin

00110111
10111110
01010000
11101011
00001111
11110001
01101001
10011001
01011110
00011100
00100100
00110110
00111010
01100111
11000000
10010000
11010010
01110010
00001010
00111101
10110010
00100001
11100111
10100100
01000010
00001111
10100010
10101011
00000011
01011011
01111000
00011011
00000001
00000000
01000011
10101011
00111100
01011111
00100000
00011110
01101010
10101101
00000110
01101100
00010101
10001000
01001110
10010101
11111101
00101101

stdout

Error in /volume/CODE:1: instantiating 'loop()'

loop{p (1+8*gets.to_i 2)**0.5%1>0?0:1}
^~~~

in /volume/CODE:1: instantiating 'loop()'

loop{p (1+8*gets.to_i 2)**0.5%1>0?0:1}
^~~~

in /volume/CODE:1: undefined method 'to_i' for Nil (compile-time type is (String | Nil)) (did you mean 'to_s'?)

loop{p (1+8*gets.to_i 2)**0.5%1>0?0:1}
                  ^~~~

Rerun with --error-trace to show a complete error trace.

stderr

strace