Given:
The term is [tex]\sqrt{-80}[/tex].
To find:
The simplified form of the given term in terms of i.
Solution:
We have,
[tex]\sqrt{-80}[/tex]
It can be written as:
[tex]\sqrt{-80}=\sqrt{80\times (-1)}[/tex]
[tex]\sqrt{-80}=\sqrt{80}\times \sqrt{-1}[/tex]
[tex]\sqrt{-80}=\sqrt{16\times 5}\times i[/tex] [tex][\because \sqrt{-1}=i][/tex]
On further simplification, we get
[tex]\sqrt{-80}=\sqrt{16}\times \sqrt{5}\times i[/tex]
[tex]\sqrt{-80}=4\times \sqrt{5}\times i[/tex]
[tex]\sqrt{-80}=4\sqrt{5}i[/tex]
Therefore, the required term is [tex]4\sqrt{5}i[/tex].
