rdmd, 131 bytes

Result

WA

Code [DL]

import std.stdio;
void main() {
string s;
while ((s=readln()).length>3){
int i=to!int(split(s)[0],2);
writeln(8*i+1)**.5,2)==1);
}}

stdin

01010100
11001001
00101101
01101001
00010101
01000111
10011011
10001101
01111000
10100000
01011011
10011001
10001000
01000011
00100011
10101100
10100110
00110111
10011010
11111101
11100111
10011111
01000010
00001010
10101011
01010110
00000000
11010010
11001111
00000001
10111110
00011100
01001110
00000110
00100100
11000011
01010101
00101101
01111011
11101100
00000011
00100110
11101010
01001010
10101110
01000101
00001111
01000010
00011011
00101110

stdout

stderr

/volume/CODE.d(6): Error: found ')' when expecting ';' following statement
/volume/CODE.d(6): Error: found '==' instead of statement
Failed: ["dmd", "-v", "-o-", "/volume/CODE.d", "-I/volume"]

strace