simplify: $\sqrt{\frac{272p^9}{324q^2}}$. write your evaluation of the square root function as a positive value.

note: assume all variables are greater than zero.

Question

simplify: $\sqrt{\frac{272p^9}{324q^2}}$. write your evaluation of the square root function as a positive value.

note: assume all variables are greater than zero.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quotient Property of Square Roots", "Simplifying Variable Radicals" ], "new_concepts": [], "current_concepts": [ "Quotient Property of Square Roots", "Simplifying Variable Radicals" ] } ## Apply the quotient property of square roots $$ \sqrt{\frac{272p^9}{324q^2}} = \frac{\sqrt{272p^9}}{\sqrt{324q^2}} $$ ## Simplify the numerator and denominator separately $$ \begin{aligned} 272 &= 16 \times 17 \ \sqrt{272p^9} &= \sqrt{16 \cdot 17 \cdot p^8 \cdot p} = 4p^4\sqrt{17p} \ \sqrt{324q^2} &= \sqrt{18^2 \cdot q^2} = 18q \end{aligned} $$ ## Reduce the resulting fraction $$ \frac{4p^4\sqrt{17p}}{18q} = \frac{2p^4\sqrt{17p}}{9q} $$ Simplify: $\sqrt{\frac{272p^9}{324q^2}}$. Write your evaluation of the square root function as a positive value. Note: Assume all variables are greater than zero. Provide your answer below: $\frac{2p^4\sqrt{17p}}{9q}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quotient Property of Square Roots" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the quotient property of square roots

Simplify the numerator and denominator separately

Reduce the resulting fraction

Answer: