To find the sum [tex]\(\sqrt{3} + 11\sqrt{12}\)[/tex], we need to simplify the terms and then combine them:
1. Simplify [tex]\(\sqrt{12}\)[/tex]:
[tex]\[\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}\][/tex]
2. Substitute [tex]\(\sqrt{12}\)[/tex] in the given expression:
[tex]\[11\sqrt{12} = 11 \cdot 2\sqrt{3} = 22\sqrt{3}\][/tex]
3. Combine the simplified terms [tex]\(\sqrt{3}\)[/tex] and [tex]\(22\sqrt{3}\)[/tex]:
[tex]\[\sqrt{3} + 22\sqrt{3} = (1 + 22)\sqrt{3} = 23\sqrt{3}\][/tex]
Therefore, the sum [tex]\(\sqrt{3} + 11\sqrt{12}\)[/tex] is [tex]\(23\sqrt{3}\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{23\sqrt{3}}
\][/tex]
