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the product of $2\sqrt{3}$ and $3\sqrt{12}$ in simplified form is .

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the product of $2\sqrt{3}$ and $3\sqrt{12}$ in simplified form is  .

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Radical Multiplication", "Simplifying Radicals" ], "current_concepts": [ "Radical Multiplication", "Simplifying Radicals" ] } ## Set up the product of the radical expressions $$ P = (2\sqrt{3}) \cdot (3\sqrt{12}) $$ ## Multiply the coefficients and the radicands $$ P = (2 \cdot 3) \cdot \sqrt{3 \cdot 12} = 6\sqrt{36} $$ ## Simplify the square root $$ P = 6 \cdot 6 = 36 $$ The product of $2\sqrt{3}$ and $3\sqrt{12}$ in simplified form is 36. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the product of the radical expressions

Multiply the coefficients and the radicands

Simplify the square root

Answer: