Answer:
The equivalent expression is [tex](4\sqrt{5})i[/tex]
Step-by-step explanation:
Given the expression [tex]\sqrt{-80}[/tex] we can use prime factorization and a property of imaginary numbers to obtain an equivalent expression.
Let's start applying prime factorization over [tex]80[/tex]
[tex]80=(2).(40)=(2).(2).(20)=(2).(2).(2).(10)=(2).(2).(2).(2).(5)=(2^{4}).(5)[/tex]
The other property is [tex]i^{2}=-1[/tex] (This is a property of imaginary numbers).
We can write [tex]-80[/tex] as
[tex]-80=(2^{4}).(5).i^{2}[/tex]
Now we apply square root to the expression ⇒
[tex]\sqrt{(2^{4}).(5).i^{2}}=(4\sqrt{5})i[/tex]
