what is the following product?

$\sqrt{30} \cdot \sqrt{10}$

* $2\sqrt{10}$
* $3\sqrt{10}$
* $4\sqrt{10}$
* $10\sqrt{3}$

Question

what is the following product?

$\sqrt{30} \cdot \sqrt{10}$

* $2\sqrt{10}$
* $3\sqrt{10}$
* $4\sqrt{10}$
* $10\sqrt{3}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Product Property of Radicals", "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Product Property of Radicals", "Radical Simplification" ] } ## 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 $$ \sqrt{300} = \sqrt{100 \cdot 3} = \sqrt{10^2 \cdot 3} = 10\sqrt{3} $$

(A) $2\sqrt{10}$

(B) $3\sqrt{10}$

(C) $4\sqrt{10}$

(D) $10\sqrt{3}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the product property of radicals

Simplify the radical expression

Answer: