To simplify the expression [tex]\(\sqrt{24} - 2 \sqrt{12} + 7 \sqrt{6}\)[/tex], let's break down the terms step-by-step.
1. First, simplify [tex]\(\sqrt{24}\)[/tex]:
[tex]\[
\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}
\][/tex]
2. Next, simplify [tex]\(2 \sqrt{12}\)[/tex]:
[tex]\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\][/tex]
Thus,
[tex]\[
2 \sqrt{12} = 2 \times 2 \sqrt{3} = 4 \sqrt{3}
\][/tex]
3. The term [tex]\(7 \sqrt{6}\)[/tex] remains as is since it is already in its simplest form.
Now, we combine the simplified terms:
[tex]\[
2 \sqrt{6} - 4 \sqrt{3} + 7 \sqrt{6}
\][/tex]
Combine the like terms involving [tex]\(\sqrt{6}\)[/tex]:
[tex]\[
(2 \sqrt{6} + 7 \sqrt{6}) - 4 \sqrt{3} = 9 \sqrt{6} - 4 \sqrt{3}
\][/tex]
So the expression in simplified form is:
[tex]\[
7 \sqrt{6} - 2 \sqrt{3}
\][/tex]
Among the given choices, the correct simplified form of the expression is:
[tex]\[
\boxed{7 \sqrt{6} - 2 \sqrt{3}}
\][/tex]
