question

simplify: $\sqrt{\frac{384u^5y}{242u^2y^{13}}}$.

note: assume all variables are greater than zero.

provide your answer below:

Question

question

simplify: $\sqrt{\frac{384u^5y}{242u^2y^{13}}}$.

note: assume all variables are greater than zero.

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Radicals", "Simplifying Variable Radicals" ], "new_concepts": [], "current_concepts": [ "Simplifying Radicals", "Simplifying Variable Radicals", "Fraction Arithmetic" ] } ## Simplify the fraction inside the radical $$ \frac{384u^5y}{242u^2y^{13}} = \frac{192u^3}{121y^{12}} $$ ## Apply the square root to the simplified fraction $$ \sqrt{\frac{192u^3}{121y^{12}}} = \frac{\sqrt{192u^3}}{\sqrt{121y^{12}}} $$ ## Simplify the numerator and denominator radicals $$ \begin{aligned} \sqrt{192u^3} &= \sqrt{64 \cdot 3 \cdot u^2 \cdot u} = 8u\sqrt{3u} \ \sqrt{121y^{12}} &= 11y^6 \ \frac{\sqrt{192u^3}}{\sqrt{121y^{12}}} &= \frac{8u\sqrt{3u}}{11y^6} \end{aligned} $$ $\frac{8u\sqrt{3u}}{11y^6}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Variable Radicals" ] }

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QUESTION IMAGE

Question

Explanation:

Simplify the fraction inside the radical

Apply the square root to the simplified fraction

Simplify the numerator and denominator radicals

Answer: