combine these radicals. (-12\\sqrt{12} - 2\\sqrt{3}) - (-50\\sqrt{3}) - (-22\\sqrt{3}) - (-26\\sqrt{3}) - (-10\\sqrt{12})

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Simplifying Radicals", "Combining Like Radicals" ], "current_concepts": [ "Simplifying Radicals", "Combining Like Radicals" ] } ## Simplify the first radical term \[ -12\sqrt{12} = -12\sqrt{4 \cdot 3} = -12 \cdot 2\sqrt{3} = -24\sqrt{3} \] ## Combine the like radical terms \[ -24\sqrt{3} - 2\sqrt{3} = (-24 - 2)\sqrt{3} = -26\sqrt{3} \] (A) $-50\sqrt{3}$ (B) $-22\sqrt{3}$ (C) $-26\sqrt{3}$ (D) $-10\sqrt{12}$ { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Radicals" ] }

combine these radicals. (-12\\sqrt{12} - 2\\sqrt{3}) - (-50\\sqrt{3}) -…

QUESTION IMAGE

$combine these radicals. (-12\\sqrt{12} - 2\\sqrt{3}) - (-50\\sqrt{3}) -…$

Question

combine these radicals.

(-12\sqrt{12} - 2\sqrt{3})

(-50\sqrt{3})
(-22\sqrt{3})
(-26\sqrt{3})
(-10\sqrt{12})

Explanation:

Response

<pre_analysis>
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"quality": "clear",
"question_count": 1,
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"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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"Simplifying Radicals",
"Combining Like Radicals"
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"Combining Like Radicals"
]
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</pre_analysis>

Simplify the first radical term

\[
-12\sqrt{12} = -12\sqrt{4 \cdot 3} = -12 \cdot 2\sqrt{3} = -24\sqrt{3}
\]

Combine the like radical terms

\[
-24\sqrt{3} - 2\sqrt{3} = (-24 - 2)\sqrt{3} = -26\sqrt{3}
\]
</reasoning>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Simplifying Radicals"
]
}
</post_analysis>

Answer: