[tex] \sqrt{-80} \\
[/tex]
We can write it as:
[tex] \sqrt{-1} \times \sqrt{80} [/tex]
Apply imaginary number rule:
[tex] \sqrt{-1} =i[/tex]
We get
[tex] =\sqrt{80} i[/tex]
Now factorise 80.
80=4 x 4 x 5 = 4² x 5
[tex] \sqrt{80}i = \sqrt{4^2 \times 5} i [/tex]
[tex] =\sqrt{4^2} \times \sqrt{5} i \\
=4 \sqrt{5} i[/tex]
[tex]Answer: \ 4 \sqrt{5} i[/tex]