College

Which choice is equivalent to the expression below?

\(\sqrt{-27}\)

A. \(-3\sqrt{3}\)

B. \(3\sqrt{3}\)

C. \(3i\sqrt{3}\)

D. \(-\sqrt{27}\)

E. \(-3\sqrt{3}i\)

Answer :

Answer:

C. 3iāœ“3

Step-by-step explanation:

Which choice is equivalent to the expression below?

āœ“-27

Square root of a negative value, so it will have a complex part.

We have that:

[tex]\sqt{-a^2} = ai[/tex]

In this question:

The square root of -27 can be factored as:

[tex]\sqrt{-27} = \sqrt{3(-9)} = \sqrt{3}\sqrt{-9} = 3i\sqrt{3}[/tex]

So the correct answer is given by option C.