what is the following product? assume $x \ge 0$ and $y \ge 0$.

$\sqrt{5x^8y^2} \cdot \sqrt{10x^3} \cdot \sqrt{12y}$

* $3x^5y\sqrt{3xy}$
* $10x^5y\sqrt{6xy}$
* $3x^3y\sqrt{3x^2y^2}$
* $10x^3y\sqrt{6x^2y^2}$

Question

what is the following product? assume $x \ge 0$ and $y \ge 0$.

$\sqrt{5x^8y^2} \cdot \sqrt{10x^3} \cdot \sqrt{12y}$

* $3x^5y\sqrt{3xy}$
* $10x^5y\sqrt{6xy}$
* $3x^3y\sqrt{3x^2y^2}$
* $10x^3y\sqrt{6x^2y^2}$

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", "Simplifying Radical Products" ], "new_concepts": [], "current_concepts": [ "Product Property of Radicals", "Radical Simplification", "Simplifying Radical Products" ] } ## Combine the radicals Using the *Product Property of Radicals* knowledge point $$ \begin{aligned} P &= \sqrt{5x^8y^2} \cdot \sqrt{10x^3} \cdot \sqrt{12y} \ P &= \sqrt{(5x^8y^2) \cdot (10x^3) \cdot (12y)} \ P &= \sqrt{600x^{11}y^3} \end{aligned} $$ ## Factor out perfect squares Using the *Radical Simplification* and *Simplifying Radical Products* knowledge points $$ \begin{aligned} 600 &= 100 \cdot 6 = 10^2 \cdot 6 \ x^{11} &= x^{10} \cdot x = (x^5)^2 \cdot x \ y^3 &= y^2 \cdot y = (y)^2 \cdot y \ P &= \sqrt{100 \cdot x^{10} \cdot y^2 \cdot 6xy} \ P &= 10x^5y\sqrt{6xy} \end{aligned} $$

(A) $3x^5y\sqrt{3xy}$

(B) $10x^5y\sqrt{6xy}$

(C) $3x^3y\sqrt{3x^2y^2}$

(D) $10x^3y\sqrt{6x^2y^2}$

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

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QUESTION IMAGE

Question

Explanation:

Combine the radicals

Factor out perfect squares

Answer: