To determine which expression simplifies to [tex]\( 3 \sqrt{11} \)[/tex], let's analyze each option.
1. [tex]\(\sqrt{14}\)[/tex]:
- The expression [tex]\(\sqrt{14}\)[/tex] cannot be simplified further, and there are no obvious factors that make it equivalent to [tex]\( 3 \sqrt{11} \)[/tex], since [tex]\( 3 \sqrt{11} = \sqrt{99} \)[/tex] which isn't equal to [tex]\(\sqrt{14}\)[/tex].
2. [tex]\(\sqrt{20}\)[/tex]:
- Similarly, [tex]\(\sqrt{20}\)[/tex] is not directly reducible to [tex]\( 3 \sqrt{11} \)[/tex]. Simplifying [tex]\(\sqrt{20}\)[/tex] gives [tex]\(\sqrt{4 \cdot 5} = 2 \sqrt{5}\)[/tex].
3. [tex]\(\sqrt{33}\)[/tex]:
- Simplifying [tex]\(\sqrt{33}\)[/tex] gives [tex]\(\sqrt{33}\)[/tex], which is not equivalent to [tex]\( 3 \sqrt{11} \)[/tex].
4. [tex]\(\sqrt{99}\)[/tex]:
- Simplifying [tex]\(\sqrt{99}\)[/tex] can be done by factoring it into [tex]\(\sqrt{9 \cdot 11} = \sqrt{9} \cdot \sqrt{11} = 3 \sqrt{11}\)[/tex].
Thus, among the given options, [tex]\(\sqrt{99}\)[/tex] simplifies exactly to [tex]\( 3 \sqrt{11} \)[/tex].
Therefore, the correct answer is:
D. [tex]\(\sqrt{99}\)[/tex]
