Respuesta :

You can factor -80 as

[tex]-80 = (-1)\cdot 16 \cdot 5[/tex]

So, we have

[tex]\sqrt{-80} = \sqrt{(-1)\cdot 16 \cdot 5}[/tex]

The square root of a product is the product of the square roots:

[tex]\sqrt{-80} = \sqrt{(-1)}\sqrt{16}\sqrt{5}[/tex]

Since [tex]i^2=-1[/tex] and [tex]4^2=16[/tex], we have

[tex]\sqrt{-80} = 4i\sqrt{5}[/tex]

The equivalent expression of the complex expression √(-80) will be 4i√5. Then the correct option is C.

What is a complex number?

A complex number is a number that is made up of both real and imaginary numbers. The complex number can be given as a + ib where a is the real part and ib is the imaginary part.

The expression is given below.

⇒ √(-80)

And we know that √(-1) = i

Then the expression can be written as

⇒ √(-1 x 16 x 5)

⇒ 4i√5

More about the complex number link is given below.

https://brainly.com/question/10251853

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