vim, 113 bytes

Result

WA

Code [DL]

00000000  71 7a 22 61 78 22 62 78  22 63 78 22 64 78 22 65  |qz"ax"bx"cx"dx"e|
00000010  78 22 66 78 22 67 78 22  68 73 12 3d 28 40 61 2a  |x"fx"gx"hs.=(@a*|
00000020  31 32 38 2b 40 62 2a 36  34 2b 40 63 2a 33 32 2b  |128+@b*64+@c*32+|
00000030  40 64 2a 31 36 2b 40 65  2a 38 2b 40 66 2a 34 2b  |@d*16+@e*8+@f*4+|
00000040  40 67 2a 32 2b 40 68 29  2a 38 2b 31 0a 1b 63 63  |@g*2+@h)*8+1..cc|
00000050  12 3d 66 6d 6f 64 28 73  71 72 74 28 40 40 29 2c  |.=fmod(sqrt(@@),|
00000060  31 29 3d 3d 30 0a 1b 6a  5e 71 34 39 40 7a 5a 5a  |1)==0..j^q49@zZZ|
00000070  0a                                                |.|
00000071

Disassembly

qz"ax"bx"cx"dx"ex"fx"gx"hs<C-R>=(@a*128+@b*64+@c*32+@d*16+@e*8+@f*4+@g*2+@h)*8+1<NL><Esc>cc<C-R>=fmod(sqrt(@@),1)==0<NL><Esc>j^q49@zZZ<NL>

stdin

01011000
01010011
10101011
00000110
01100100
00110111
01101111
11111010
01001111
10101010
11111110
01111010
00011110
00100100
10001101
10001000
00011100
01001110
10001111
01110011
00101101
11111101
00000000
11000010
01111000
01010010
11111101
00001111
01011011
00010010
00010011
10011001
00001010
11100111
01000010
10111110
00010101
11000111
01101001
10101101
00000111
01101100
11010010
10100100
01000001
00000001
10011001
00110100
00000011
10011100

stdout

01011000
01010011
10101011
00000110
01100100
00110111
01101111
11111010
01001111
10101010
11111110
01111010
00011110
00100100
10001101
10001000
00011100
01001110
10001111
01110011
00101101
11111101
00000000
11000010
01111000
01010010
11111101
00001111
01011011
00010010
00010011
10011001
00001010
11100111
01000010
10111110
00010101
11000111
01101001
10101101
00000111
01101100
11010010
10100100
01000001
00000001
10011001
00110100
00000011
10011100

stderr

strace