we know that
[tex]i^{2} =-1[/tex]
we have
[tex]\sqrt{-16} =\sqrt{(-1)*(16)} =\sqrt{(-1)*(4^{2})}[/tex]
substitute the value of [tex]i^{2}=-1[/tex] in the expression above
[tex]\sqrt{(-1)*(4^{2})}=\sqrt{i^{2}*4^{2}} \\ \\= 4i[/tex]
therefore
the answer is
[tex]4i[/tex]
