multiplying $\frac{3}{\sqrt{17}-\sqrt{2}}$ by which fraction will produce an equivalent fraction with a rational denominator?

$\circ$ $\frac{\sqrt{17}-\sqrt{2}}{\sqrt{17}-\sqrt{2}}$

$\circ$ $\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}$

$\circ$ $\frac{\sqrt{2}-\sqrt{17}}{\sqrt{2}-\sqrt{17}}$

$\circ$ $\frac{\sqrt{15}}{\sqrt{15}}$

Question

multiplying $\frac{3}{\sqrt{17}-\sqrt{2}}$ by which fraction will produce an equivalent fraction with a rational denominator?

$\circ$ $\frac{\sqrt{17}-\sqrt{2}}{\sqrt{17}-\sqrt{2}}$

$\circ$ $\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}$

$\circ$ $\frac{\sqrt{2}-\sqrt{17}}{\sqrt{2}-\sqrt{17}}$

$\circ$ $\frac{\sqrt{15}}{\sqrt{15}}$

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 *Rationalizing the Denominator* and *Radical Conjugates* knowledge points $$ \begin{aligned} &\text{Given expression: } \frac{3}{\sqrt{17} - \sqrt{2}}\ &\text{Denominator: } \sqrt{17} - \sqrt{2}\ &\text{Conjugate of denominator: } \sqrt{17} + \sqrt{2} \end{aligned} $$ ## Determine the rationalizing fraction Using the *Rationalizing the Denominator* knowledge point $$ \begin{aligned} &\text{To rationalize, multiply numerator and denominator by the conjugate:}\ &\text{Fraction to multiply: } \frac{\sqrt{17} + \sqrt{2}}{\sqrt{17} + \sqrt{2}} \end{aligned} $$

(A) $\frac{\sqrt{17} - \sqrt{2}}{\sqrt{17} - \sqrt{2}}$

(B) $\frac{\sqrt{17} + \sqrt{2}}{\sqrt{17} + \sqrt{2}}$

(C) $\frac{\sqrt{2} - \sqrt{17}}{\sqrt{2} - \sqrt{17}}$

(D) $\frac{\sqrt{15}}{\sqrt{15}}$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the denominator and its conjugate

Determine the rationalizing fraction

Answer: