vim, 120 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 70 6f 77 28 66 6c  6f 6f 72 28 73 71 72 74  |.=pow(floor(sqrt|
00000060  28 40 40 29 29 2c 32 29  3d 3d 40 40 0a 1b 6a 5e  |(@@)),2)==@@..j^|
00000070  71 34 39 40 7a 5a 5a 0a                           |q49@zZZ.|
00000078

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>=pow(floor(sqrt(@@)),2)==@@<NL><Esc>j^q49@zZZ<NL>

stdin

00000000
11111101
10101010
00001010
00101101
00100100
00101011
11011000
00001111
00100100
00000011
10111111
01101010
10101100
00010010
11100111
10001110
01000010
01001110
01011011
00000001
01001111
00110111
10111101
01100010
00011100
11010010
11101000
11110110
01110110
01011100
10011011
00101111
10101000
00100100
10001000
01111110
00000110
10110100
11101100
00110000
00100010
01111000
10101011
10111110
10011001
00010101
00100110
01101001
01100000

stdout

00000000
11111101
10101010
00001010
00101101
00100100
00101011
11011000
00001111
00100100
00000011
10111111
01101010
10101100
00010010
11100111
10001110
01000010
01001110
01011011
00000001
01001111
00110111
10111101
01100010
00011100
11010010
11101000
11110110
01110110
01011100
10011011
00101111
10101000
00100100
10001000
01111110
00000110
10110100
11101100
00110000
00100010
01111000
10101011
10111110
10011001
00010101
00100110
01101001
01100000

stderr

strace