question

simplify: $\sqrt3{27d^{18}}$.

provide your answer below:

Question

question

simplify: $\sqrt3{27d^{18}}$.

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 Cube Roots" ], "new_concepts": [], "current_concepts": [ "Simplifying Cube Roots", "Simplifying Radicals", "Simplifying Variable Radicals" ] } ## Separate the radical into numerical and variable factors $$ \sqrt[3]{27d^{18}} = \sqrt[3]{27} \cdot \sqrt[3]{d^{18}} $$ ## Simplify each cube root factor $$ \begin{aligned} \sqrt[3]{27} &= \sqrt[3]{3^3} = 3 \ \sqrt[3]{d^{18}} &= d^{\frac{18}{3}} = d^6 \end{aligned} $$ ## Multiply the simplified factors $$ 3 \cdot d^6 = 3d^6 $$ Simplify: $\sqrt[3]{27d^{18}}$. Provide your answer below: $3d^6$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Cube Roots" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Separate the radical into numerical and variable factors

Simplify each cube root factor

Multiply the simplified factors

Answer: