#C, 64 bytes

Call f() with the string to square.

m;f(char*s){for(m=sqrt(strlen(s));*s;s+=m)printf("%.*s\n",m,s);}

Try it on ideone.

C, 64 bytes

Call f() with the string to square.

m;f(char*s){for(m=sqrt(strlen(s));*s;s+=m)printf("%.*s\n",m,s);}

Try it on ideone.

#C, 65 bytes

Call f() with the string to square.

m;f(char*s){for(m=sqrt(strlen(s));*s;printf("%.*s\n",m,s),s+=m);}

Try it on ideone.

#C, 64 bytes

Call f() with the string to square.

m;f(char*s){for(m=sqrt(strlen(s));*s;s+=m)printf("%.*s\n",m,s);}

Try it on ideone.