Question

what is the following product?

\\(\sqrt{30} \cdot \sqrt{10}\\)

• \\(2\sqrt{10}\\)
• \\(3\sqrt{10}\\)
• \\(4\sqrt{10}\\)
• \\(10\sqrt{3}\\)

Explanation:

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"concepts_used": [
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<reasoning>

Apply the product property of radicals

Using the Product Property of Radicals knowledge point
\[
\sqrt{30} \cdot \sqrt{10} = \sqrt{30 \cdot 10} = \sqrt{300}
\]

Simplify the radical expression

Using the Radical Simplification knowledge point
\[
\sqrt{300} = \sqrt{100 \cdot 3} = \sqrt{10^2 \cdot 3} = 10\sqrt{3}
\]
</reasoning>

<answer>
<mcq-option>(A) \(2\sqrt{10}\)</mcq-option>
<mcq-option>(B) \(3\sqrt{10}\)</mcq-option>
<mcq-option>(C) \(4\sqrt{10}\)</mcq-option>
<mcq-correct>(D) \(10\sqrt{3}\)</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Radical Simplification"
]
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Answer:

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</pre_analysis>

<reasoning>

Apply the product property of radicals

Using the Product Property of Radicals knowledge point
\[
\sqrt{30} \cdot \sqrt{10} = \sqrt{30 \cdot 10} = \sqrt{300}
\]

Simplify the radical expression

Using the Radical Simplification knowledge point
\[
\sqrt{300} = \sqrt{100 \cdot 3} = \sqrt{10^2 \cdot 3} = 10\sqrt{3}
\]
</reasoning>

<answer>
<mcq-option>(A) \(2\sqrt{10}\)</mcq-option>
<mcq-option>(B) \(3\sqrt{10}\)</mcq-option>
<mcq-option>(C) \(4\sqrt{10}\)</mcq-option>
<mcq-correct>(D) \(10\sqrt{3}\)</mcq-correct>
</answer>

<post_analysis>
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"question_type": "Multiple Choice",
"knowledge_point": [
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"Algebra",
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]
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