to rationalize the denominator of $\frac{5 - \sqrt{7}}{9 - \sqrt{14}}$, you should multiply the expression by which fraction?

$\circ$ $\frac{5 + \sqrt{7}}{9 - \sqrt{14}}$

$\circ$ $\frac{9 - \sqrt{14}}{9 - \sqrt{14}}$

$\circ$ $\frac{9 + \sqrt{14}}{9 + \sqrt{14}}$

$\circ$ $\frac{\sqrt{14}}{\sqrt{14}}$

Question

to rationalize the denominator of $\frac{5 - \sqrt{7}}{9 - \sqrt{14}}$, you should multiply the expression by which fraction?

$\circ$ $\frac{5 + \sqrt{7}}{9 - \sqrt{14}}$

$\circ$ $\frac{9 - \sqrt{14}}{9 - \sqrt{14}}$

$\circ$ $\frac{9 + \sqrt{14}}{9 + \sqrt{14}}$

$\circ$ $\frac{\sqrt{14}}{\sqrt{14}}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Rationalizing the Denominator", "Radical Conjugates" ], "new_concepts": [], "current_concepts": [ "Rationalizing the Denominator", "Radical Conjugates" ] } ## Identify the denominator and its conjugate Using the *Radical Conjugates* knowledge point $$ \begin{aligned} &\text{Denominator: } 9 - \sqrt{14}\ &\text{Conjugate: } 9 + \sqrt{14} \end{aligned} $$ ## Determine the rationalizing fraction Using the *Rationalizing the Denominator* knowledge point $$ \frac{9 + \sqrt{14}}{9 + \sqrt{14}} $$

(A) $\frac{5 + \sqrt{7}}{9 - \sqrt{14}}$

(B) $\frac{9 - \sqrt{14}}{9 - \sqrt{14}}$

(C) $\frac{9 + \sqrt{14}}{9 + \sqrt{14}}$

(D) $\frac{\sqrt{14}}{\sqrt{14}}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rationalizing the Denominator" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the denominator and its conjugate

Determine the rationalizing fraction

Answer: