bash-pure, 83 bytes

Result

AC

Code [DL]

while read a;do b=$[2#$a*8+1];for ((c=$b;c*c>b;c--));do :;done;echo $[c*c==b];done;

stdin

00010000
01110100
00011010
11110101
01110110
01001011
11110001
01000010
00011100
11111101
00000110
01011110
00010100
00000000
00001010
01100100
01101001
01110000
00110101
01111000
10011001
01001110
10011100
00100010
01011011
00101010
01110001
10101011
11011011
11010010
10101011
11000100
00101101
00000001
10111110
00110010
00100100
00010101
00001111
01010101
00110111
00000100
11110010
01111000
11110011
11100101
10001000
00000011
11100111
10111101

stdout

0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0

stderr

/bin/bash: warning: setlocale: LC_ALL: cannot change locale (en_US.UTF-8)

strace