To find the conjugate of the expression [tex]\(\sqrt{x-5} - 2\)[/tex], we need to form an expression where the sign between the two terms is changed. Here, the original expression is:
[tex]\[
\sqrt{x-5} - 2
\][/tex]
The conjugate of an expression of the form [tex]\(a - b\)[/tex] is [tex]\(a + b\)[/tex]. Denote [tex]\(a = \sqrt{x-5}\)[/tex] and [tex]\(b = 2\)[/tex].
By changing the sign from minus to plus, the conjugate expression becomes:
[tex]\[
\sqrt{x-5} + 2
\][/tex]
Therefore, the correct choice is:
[tex]\[
\text{C. } \sqrt{x-5} + 2
\][/tex]
Thus, the conjugate of [tex]\(\sqrt{x-5} - 2\)[/tex] is [tex]\(\sqrt{x-5} + 2\)[/tex]. The answer is C.
