question 12 (3 points)

simplify $11\sqrt{63} - 4\sqrt{63} - 13\sqrt{20}$

Question

question 12 (3 points)

simplify $11\sqrt{63} - 4\sqrt{63} - 13\sqrt{20}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Radicals", "Operations with Radicals" ], "new_concepts": [], "current_concepts": [ "Simplifying Radicals", "Operations with Radicals" ] } ## Combine like radical terms $$ 11\sqrt{63} - 4\sqrt{63} - 13\sqrt{20} = 7\sqrt{63} - 13\sqrt{20} $$ ## Simplify each radical term $$ \begin{aligned} 7\sqrt{63} &= 7\sqrt{9 \times 7} = 7 \times 3\sqrt{7} = 21\sqrt{7} \ 13\sqrt{20} &= 13\sqrt{4 \times 5} = 13 \times 2\sqrt{5} = 26\sqrt{5} \end{aligned} $$ ## Write the final simplified expression $$ 21\sqrt{7} - 26\sqrt{5} $$ $21\sqrt{7} - 26\sqrt{5}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Operations with Radicals" ] }

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Question

Explanation:

Combine like radical terms

Simplify each radical term

Write the final simplified expression

Answer: