current objective
use the product property to simplify square roots

question

simplify: $\sqrt{171x^9y^{19}}$. assume that $x 0$ and $y 0$

provide your answer below:

Question

current objective
use the product property to simplify square roots

question

simplify: $\sqrt{171x^9y^{19}}$. assume that $x > 0$ and $y > 0$

provide your answer below:

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Radicals", "Simplifying Variable Radicals" ], "new_concepts": [], "current_concepts": [ "Simplifying Radicals", "Simplifying Variable Radicals" ] } ## Factor the radicand into perfect squares and remaining factors $$ \begin{aligned} 171 &= 9 \times 19 = 3^2 \times 19 \ x^9 &= x^8 \times x = (x^4)^2 \times x \ y^{19} &= y^{18} \times y = (y^9)^2 \times y \end{aligned} $$ ## Apply the product property of square roots $$ \begin{aligned} \sqrt{171x^9y^{19}} &= \sqrt{(9 \cdot x^8 \cdot y^{18}) \cdot (19 \cdot x \cdot y)} \ &= \sqrt{9x^8y^{18}} \cdot \sqrt{19xy} \end{aligned} $$ ## Simplify the perfect square radical $$ \sqrt{9x^8y^{18}} \cdot \sqrt{19xy} = 3x^4y^9\sqrt{19xy} $$ Simplify: $\sqrt{171x^9y^{19}}$. Assume that $x > 0$ and $y > 0$ Provide your answer below: $3x^4y^9\sqrt{19xy}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Variable Radicals" ] }

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QUESTION IMAGE

Question

Explanation:

Factor the radicand into perfect squares and remaining factors

Apply the product property of square roots

Simplify the perfect square radical

Answer: