powershell, 56 bytes

Result

WA

Code [DL]

$_|%{+([Math]::Sqrt([Convert]::ToByte($_,2)*8+1)%1-eq0)}

stdin

10010000
10001000
00000011
10101001
11001000
10110111
00110111
01001110
00000101
00000000
00111111
11010010
11001111
00010001
00001111
00001010
00111101
11001101
10111110
00101101
10011001
00100100
00110100
11000001
10011101
10100110
00010010
10101011
01101111
01000010
01111000
01101101
00111010
11110100
01111110
01011011
01010111
11100111
11111101
11010010
10011100
00000110
00000000
01000000
00000001
01101001
00010101
10100001
00011100
01100111

stdout

stderr

Exception calling "ToByte" with "2" argument(s): "Index was out of range. Must 
be non-negative and less than the size of the collection.
Parameter name: startIndex"
At line:1 char:6
+ $_|%{+([Math]::Sqrt([Convert]::ToByte($_,2)*8+1)%1-eq0)}
+      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : NotSpecified: (:) [], MethodInvocationException
    + FullyQualifiedErrorId : ArgumentOutOfRangeException
 

strace