To simplify the given expression [tex]\(\sqrt{-27}\)[/tex], proceed as follows:
1. Identify the imaginary unit [tex]\(i\)[/tex]: Recall that [tex]\(i\)[/tex] is defined as [tex]\(\sqrt{-1}\)[/tex]. Therefore, [tex]\(\sqrt{-27}\)[/tex] can be rewritten using [tex]\(i\)[/tex]:
[tex]\[
\sqrt{-27} = \sqrt{27 \cdot (-1)} = \sqrt{27} \cdot \sqrt{-1} = \sqrt{27} \cdot i
\][/tex]
2. Simplify [tex]\(\sqrt{27}\)[/tex]: The number 27 can be factored into [tex]\(3^3\)[/tex]. This allows us to simplify the square root:
[tex]\[
\sqrt{27} = \sqrt{3^3} = \sqrt{3^2 \cdot 3} = \sqrt{3^2} \cdot \sqrt{3} = 3 \sqrt{3}
\][/tex]
3. Combine the results: Substitute back into our expression:
[tex]\[
\sqrt{-27} = 3 \sqrt{3} \cdot i = 3 i \sqrt{3}
\][/tex]
Therefore, the expression [tex]\(\sqrt{-27}\)[/tex] simplifies to [tex]\(3 i \sqrt{3}\)[/tex].
The equivalent choice for this expression is:
[tex]\[
\boxed{3 i \sqrt{3}}
\][/tex]
Hence, the correct choice is:
[tex]\[
\boxed{E}
\][/tex]
