simplify the following radical expression.

$(1 + 2\sqrt{7})(3 + 4\sqrt{7})$

$? + \sqrt{ }$

Question

simplify the following radical expression.

$(1 + 2\sqrt{7})(3 + 4\sqrt{7})$

$? +  \sqrt{ }$

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" ] } ## Expand the expression using FOIL $$ (1 + 2\sqrt{7})(3 + 4\sqrt{7}) = 1 \cdot 3 + 1 \cdot 4\sqrt{7} + 2\sqrt{7} \cdot 3 + 2\sqrt{7} \cdot 4\sqrt{7} $$ ## Simplify individual terms $$ \begin{aligned} 1 \cdot 3 &= 3 \ 1 \cdot 4\sqrt{7} &= 4\sqrt{7} \ 2\sqrt{7} \cdot 3 &= 6\sqrt{7} \ 2\sqrt{7} \cdot 4\sqrt{7} &= 8 \cdot 7 = 56 \end{aligned} $$ ## Combine like terms $$ \begin{aligned} (3 + 56) + (4\sqrt{7} + 6\sqrt{7}) &= 59 + 10\sqrt{7} \end{aligned} $$ Simplify the following radical expression. $$(1 + 2\sqrt{7})(3 + 4\sqrt{7})$$ 59 + 10$\sqrt{\text{7}}$ { "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 FOIL

Simplify individual terms

Combine like terms

Answer: