To simplify the expression [tex]\(\sqrt{5}(6 - 4\sqrt{3})\)[/tex], we can follow these steps:
1. Distribute [tex]\(\sqrt{5}\)[/tex] through the expression inside the parentheses:
[tex]\[
\sqrt{5}(6 - 4\sqrt{3})
\][/tex]
2. Distribute [tex]\(\sqrt{5}\)[/tex] to each term inside the parentheses separately:
[tex]\[
\sqrt{5} \cdot 6 - \sqrt{5} \cdot 4\sqrt{3}
\][/tex]
3. Multiply [tex]\(\sqrt{5}\)[/tex] with 6:
[tex]\[
6\sqrt{5}
\][/tex]
4. Multiply [tex]\(\sqrt{5}\)[/tex] with [tex]\(4\sqrt{3}\)[/tex]:
[tex]\[
4\sqrt{5} \cdot \sqrt{3}
\][/tex]
5. Combine the square roots:
[tex]\[
4\sqrt{15}
\][/tex]
6. Combine the expressions from steps 3 and 5:
[tex]\[
6\sqrt{5} - 4\sqrt{15}
\][/tex]
Hence, the simplified form of the expression [tex]\(\sqrt{5}(6 - 4\sqrt{3})\)[/tex] is:
[tex]\[
6\sqrt{5} - 4\sqrt{15}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{6\sqrt{5} - 4\sqrt{15}}
\][/tex]
