choose the expression that shows the correct product for $\sqrt{3} \cdot \sqrt{12}$.

$\sqrt{15}$
$\sqrt{36}$
$\sqrt4{15}$
$\sqrt4{36}$

Question

choose the expression that shows the correct product for $\sqrt{3} \cdot \sqrt{12}$.

$\sqrt{15}$
$\sqrt{36}$
$\sqrt4{15}$
$\sqrt4{36}$

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": [ "Radical Expressions" ], "new_concepts": [], "current_concepts": [ "Radical Expressions", "Radical Simplification" ] } ## Apply the product rule for radicals Using the *Radical Expressions* knowledge point $$ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \quad \text{for } a, b \ge 0 $$ ## Calculate the product inside the radical Using the *Radical Expressions* knowledge point $$ \sqrt{3} \cdot \sqrt{12} = \sqrt{3 \cdot 12} = \sqrt{36} $$

(A) $\sqrt{15}$

(B) $\sqrt{36}$

(C) $\sqrt[4]{15}$

(D) $\sqrt[4]{36}$

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

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QUESTION IMAGE

Question

Explanation:

Apply the product rule for radicals

Calculate the product inside the radical

Answer: