php, 60 bytes

Result

WA

Code [DL]

<? for(;$c=fgets(STDIN);)echo+!fmod(sqrt(8*bindec($c)+1),1);

stdin

00001010
00110111
10100000
10111110
00001111
00110000
11110101
00001010
00001100
11000100
00101101
00000110
01011011
00110101
10101011
10111110
11000000
11111101
11101110
00000011
10001000
01111000
11010011
01110111
01000010
00111001
11100111
00000001
10011010
00010111
11100100
00100100
01101001
11011110
11010010
01001110
11111000
01111001
01000001
00011110
10001010
01101111
00010101
10011001
00011100
10000101
01000101
00000000
00110100
11001111

stdout

<? for(;$c=fgets(STDIN);)echo+!fmod(sqrt(8*bindec($c)+1),1);

stderr

strace