To determine which choice is the conjugate of the expression [tex]\( 5 - \sqrt{x + 4} \)[/tex], let's first recall what a conjugate is in the context of radical expressions.
The conjugate of an expression that includes a square root is typically formed by changing the sign of the term with the square root. In this case, the term with the square root in the given expression [tex]\( 5 - \sqrt{x + 4} \)[/tex] is [tex]\( -\sqrt{x + 4} \)[/tex].
Following this rule, the conjugate of [tex]\( 5 - \sqrt{x + 4} \)[/tex] can be found by changing the sign before the square root term, giving us:
[tex]\[ 5 + \sqrt{x + 4} \][/tex]
Now let's compare this result with the provided choices:
- A. [tex]\( 5 + \sqrt{x + 4} \)[/tex]
- B. [tex]\( 5 - \sqrt{x + 4} \)[/tex]
- C. [tex]\( 5 + \sqrt{x - 4} \)[/tex]
- D. [tex]\( 5 - \sqrt{x - 4} \)[/tex]
The correct conjugate of the expression [tex]\( 5 - \sqrt{x + 4} \)[/tex] is:
[tex]\[ 5 + \sqrt{x + 4} \][/tex]
So, the correct choice is:
[tex]\[ \boxed{A} \][/tex]
