Pregunta
Simplify. \( \begin{array}{l}-3 \sqrt{3}+8 \sqrt{12} \\ \text { Select the correct choice below and fill in any answer boxes in your choice. } \\ \text { A. }-3 \sqrt{3}+8 \sqrt{12}= \\ \quad \text { (Simplify your answer. Type an exact answer, using radicals as needed.) } \\ \text { B. The expression cannot be simplified. }\end{array} \) ?
Ask by Morgan Kelley. in the United States
Mar 12,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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\( -3\sqrt{3} + 8\sqrt{12} = 13\sqrt{3} \)
Solución
Calculate or simplify the expression \( -3\sqrt{3}+8\sqrt{12} \).
Calculate the value by following steps:
- step0: Calculate:
\(-3\sqrt{3}+8\sqrt{12}\)
- step1: Simplify the root:
\(-3\sqrt{3}+8\times 2\sqrt{3}\)
- step2: Multiply the terms:
\(-3\sqrt{3}+16\sqrt{3}\)
- step3: Collect like terms:
\(\left(-3+16\right)\sqrt{3}\)
- step4: Add the numbers:
\(13\sqrt{3}\)
The simplified form of the expression \(-3\sqrt{3}+8\sqrt{12}\) is \(13\sqrt{3}\).
Therefore, the correct choice is A. \(13\sqrt{3}\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución The Deep Dive
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 \( \boxed{13\sqrt{3}} \).
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