Can't make C++ program use high enough precision

...
cout << setprecision(100) << pow((3+sqrt(5.0)),28) << endl;
...

outputs

135565048129406451712

which isn't precise enough but.

$ bc <<< "scale = 100; (3+sqrt(5.0))^28"

outputs

135565048129406369791.9994684648068789538123313610677119237534230237579838585720347675878761558402979025019238688523799354

which is what I want. I'm setting the cout precision so it must be the sqrt, pow or + are losing the precision?