study the example below for the product of conjugate pairs.
$(3 + \sqrt{7})(3 - \sqrt{7})$
$= 9 - 3\sqrt{7} + 3\sqrt{7} - 7$
$= 9 - 7$
$= 2$

now, find the product $(2 + \sqrt{5})(2 - \sqrt{5})$.

the product is

Question

study the example below for the product of conjugate pairs.
$(3 + \sqrt{7})(3 - \sqrt{7})$
$= 9 - 3\sqrt{7} + 3\sqrt{7} - 7$
$= 9 - 7$
$= 2$

now, find the product $(2 + \sqrt{5})(2 - \sqrt{5})$.

the product is

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Radical Conjugates", "Multiplying Binomial Radicals" ], "new_concepts": [], "current_concepts": [ "Radical Conjugates", "Multiplying Binomial Radicals" ] } ## Expand the product of conjugates Using the *Radical Conjugates* and *Multiplying Binomial Radicals* knowledge points $$ (2+\sqrt{5})(2-\sqrt{5}) = 2(2) - 2\sqrt{5} + 2\sqrt{5} - \sqrt{5}\sqrt{5} $$ ## Simplify the terms Using the *Multiplying Binomial Radicals* knowledge point $$ \begin{aligned} &= 4 - 5\ &= -1 \end{aligned} $$ Now, find the product $(2+\sqrt{5})(2-\sqrt{5})$. The product is -1 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Radical Conjugates" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the product of conjugates

Simplify the terms

Answer: