Simplify. \( \begin{array}{l}-3 \sqrt{3}+8 \sqrt{12} \\ \text { Select the correct choice below and fill in any answer boxes in your choice. } \\ \text { A. }-3 \sqrt{3}+8 \sqrt{12}= \\ \quad \text { (Simplify your answer. Type an exact answer, using radicals as needed.) } \\ \text { B. The expression cannot be simplified. }\end{array} \) ?
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To simplify the expression \(-3 \sqrt{3} + 8 \sqrt{12}\), we start by simplifying \(\sqrt{12}\). We can express \(\sqrt{12}\) as \(\sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}\). Therefore: \[ 8 \sqrt{12} = 8 \times 2\sqrt{3} = 16\sqrt{3} \] Now, we can rewrite the original expression: \[ -3 \sqrt{3} + 16\sqrt{3} = (16 - 3)\sqrt{3} = 13\sqrt{3} \] Thus, the simplified form of the expression is: \[ -3 \sqrt{3} + 8 \sqrt{12} = 13\sqrt{3} \] So the final answer is \( \boxed{13\sqrt{3}} \).