[tex]i=\sqrt{-1}\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a}=b\iff b^2=a\\--------------------\\\\\sqrt{-16}=\sqrt{(16)(-1)}=\sqrt{16}\cdot\sqrt{-1}=4\cdot i=4i\\\\\sqrt{49}=7\ because\ 7^2=49\\\sqrt{16}=4\ because\ 4^2=16\\--------------------\\\\\sqrt{-16}+\sqrt{49}=\sqrt{49}+\sqrt{-16}=\boxed{7+4i}[/tex]
