simplify the following radical expression.

$(6 + 2\sqrt{5})(4\sqrt{5} - 5)$

$? + \quad\sqrt{\quad}$

Question

simplify the following radical expression.

$(6 + 2\sqrt{5})(4\sqrt{5} - 5)$

$? + \quad\sqrt{\quad}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Multiplying Radicals", "Combining Like Radicals" ], "new_concepts": [], "current_concepts": [ "Multiplying Radicals", "Combining Like Radicals", "Simplifying Radicals" ] } ## Expand the expression using the FOIL method $$ (6 + 2\sqrt{5})(4\sqrt{5} - 5) = 6(4\sqrt{5}) + 6(-5) + (2\sqrt{5})(4\sqrt{5}) + (2\sqrt{5})(-5) $$ ## Multiply individual terms $$ \begin{aligned} 6(4\sqrt{5}) &= 24\sqrt{5} \ 6(-5) &= -30 \ (2\sqrt{5})(4\sqrt{5}) &= 8 \times 5 = 40 \ (2\sqrt{5})(-5) &= -10\sqrt{5} \end{aligned} $$ ## Combine like terms $$ \begin{aligned} (40 - 30) + (24\sqrt{5} - 10\sqrt{5}) &= 10 + 14\sqrt{5} \end{aligned} $$ Simplify the following radical expression. $$(6 + 2\sqrt{5})(4\sqrt{5} - 5)$$ 10 + 14$\sqrt{\text{5}}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Multiplying Radicals" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the expression using the FOIL method

Multiply individual terms

Combine like terms

Answer: