vim, 42 bytes

Result

WA

Code [DL]

:%s/.\+/\=sqrt(("0b".submatch(0))*8+1)/
ZZ

Disassembly

:%s/.\+/\=sqrt(("0b".submatch(0))*8+1)/<NL>ZZ

stdin

01100101
11010010
01110010
10001010
11000111
10101101
11111101
10001000
01011100
11000001
01000111
00110111
10011100
11101011
01101111
01101001
00000001
00011111
01000010
01111000
00010101
10100000
11001010
01010110
01011011
01001110
10101011
00000000
11100111
10000001
11001101
10111110
10001101
00010100
10011110
00000011
00111100
00001111
00101101
11111101
01011001
00000110
00100000
00100110
00100100
10011001
00001010
10001000
11011110
00011100

stdout

28.442925
41.0
30.21589
33.24154
39.912404
37.215588
45.0
33.0
27.147744
39.306488
23.853721
21.0
35.341194
43.370497
29.816103
29.0
3.0
15.779734
23.0
31.0
13.0
35.79106
40.211939
26.248809
27.0
25.0
37.0
1.0
43.0
32.140317
40.509258
39.0
33.600595
12.688578
35.566838
5.0
21.931712
11.0
19.0
45.0
26.70206
7.0
16.03122
17.464249
17.0
35.0
9.0
33.0
42.154478
15.0

stderr

strace