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