simplify. (assume all variables represent positive numbers.)

\\sqrt{81(6f+1)^2}\

Question

simplify. (assume all variables represent positive numbers.)

\\sqrt{81(6f+1)^2}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Expressions" ], "new_concepts": [ "Radical Simplification" ], "current_concepts": [ "Simplifying Expressions", "Radical Simplification" ] } ## Apply product property of radicals $$ \sqrt{81(6f+1)^2} = \sqrt{81} \cdot \sqrt{(6f+1)^2} $$ ## Simplify individual square roots $$ \begin{aligned} \sqrt{81} &= 9 \ \sqrt{(6f+1)^2} &= |6f+1| \end{aligned} $$ ## Apply positive variable assumption Using the assumption that $f > 0$: $$ \begin{aligned} 6f + 1 &> 0 \ |6f+1| &= 6f+1 \ 9 \cdot (6f+1) &= 54f + 9 \end{aligned} $$ $54f + 9$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Simplification" ] }

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QUESTION IMAGE

Question

Explanation:

Apply product property of radicals

Simplify individual square roots

Apply positive variable assumption

Answer: