d) $4\sqrt{5} - 2\sqrt{2} + 8\sqrt{2}$

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Radicals" ], "new_concepts": [ "Combining Like Radicals" ], "current_concepts": [ "Simplifying Radicals", "Combining Like Radicals" ] } ## Identify like radicals $$ 4\sqrt{5} - 2\sqrt{2} + 8\sqrt{2} $$ ## Combine coefficients of like radicals $$ (-2 + 8)\sqrt{2} = 6\sqrt{2} $$ ## Write the simplified expression $$ 4\sqrt{5} + 6\sqrt{2} $$ $4\sqrt{5} + 6\sqrt{2}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Combining Like Radicals" ] }

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Explanation:

Identify like radicals

Combine coefficients of like radicals

Write the simplified expression

Answer: