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

10101111
11110001
00010101
00010101
01111000
10001001
10000110
11111101
01101100
11100111
11011010
10111110
10111100
11001100
10110011
11010101
01100001
00000001
00000000
11000100
10101011
11000110
01011011
00010011
01001110
00001010
00100100
00010001
01111110
01111111
00001111
00110111
10110101
00011100
01001010
10011001
01101001
01110000
01000000
00101101
00000011
10001000
00010010
01100000
01000010
11010010
00000110
10111010
00111010
01011011

stdout

10101111
11110001
00010101
00010101
01111000
10001001
10000110
11111101
01101100
11100111
11011010
10111110
10111100
11001100
10110011
11010101
01100001
00000001
00000000
11000100
10101011
11000110
01011011
00010011
01001110
00001010
00100100
00010001
01111110
01111111
00001111
00110111
10110101
00011100
01001010
10011001
01101001
01110000
01000000
00101101
00000011
10001000
00010010
01100000
01000010
11010010
00000110
10111010
00111010
01011011

stderr

strace