To simplify the expression [tex]\(-5 - \sqrt{-44}\)[/tex], we need to handle the square root of the negative number. Recall that the square root of a negative number involves imaginary numbers. Specifically,
[tex]\[
\sqrt{-a} = i\sqrt{a}
\][/tex]
where [tex]\(i\)[/tex] is the imaginary unit with [tex]\(i^2 = -1\)[/tex].
Let's start by simplifying [tex]\(\sqrt{-44}\)[/tex].
[tex]\[
\sqrt{-44} = \sqrt{-1 \cdot 44} = \sqrt{-1} \cdot \sqrt{44} = i \cdot \sqrt{44}
\][/tex]
Next, we simplify [tex]\(\sqrt{44}\)[/tex]. Since 44 can be factorized as [tex]\(4 \cdot 11\)[/tex], we get:
[tex]\[
\sqrt{44} = \sqrt{4 \cdot 11} = \sqrt{4} \cdot \sqrt{11} = 2 \cdot \sqrt{11}
\][/tex]
Putting it all together, we have:
[tex]\[
\sqrt{-44} = i \cdot \sqrt{44} = i \cdot (2\sqrt{11}) = 2i\sqrt{11}
\][/tex]
Now, substitute this back into our original expression:
[tex]\[
-5 - \sqrt{-44} = -5 - 2i\sqrt{11}
\][/tex]
Thus, the simplified form of [tex]\(-5 - \sqrt{-44}\)[/tex] is:
[tex]\[
-5 - 2i\sqrt{11}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-5 - 2i\sqrt{11}}
\][/tex]
