Question

Which expression is equivalent to square root of -80

Answer 1

sqrt(-80) = 8.94427191i
Hope it helped :d

Answer 2

The equivalent expression is
`(4√(5))i`

Explanation:

Given the expression
`√(-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√(5))i`