which expression should you multiply the numerator and denominator of $\frac{\sqrt3{3}}{\sqrt3{2x}}$ by to rationalize the denominator?

$\sqrt3{x^2}$
$\sqrt3{4x}$
$\sqrt3{4x^2}$
$\sqrt3{2x}$

what is $\frac{\sqrt3{3}}{\sqrt3{2x}}$ in simplest form?

$\frac{\sqrt3{12x^2}}{2x}$
$\frac{\sqrt3{6x}}{2x}$
$\frac{\sqrt3{3}}{2x}$

Question

which expression should you multiply the numerator and denominator of $\frac{\sqrt3{3}}{\sqrt3{2x}}$ by to rationalize the denominator?

$\sqrt3{x^2}$
$\sqrt3{4x}$
$\sqrt3{4x^2}$
$\sqrt3{2x}$

what is $\frac{\sqrt3{3}}{\sqrt3{2x}}$ in simplest form?

$\frac{\sqrt3{12x^2}}{2x}$
$\frac{\sqrt3{6x}}{2x}$
$\frac{\sqrt3{3}}{2x}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Rationalizing the Denominator" ], "new_concepts": [], "current_concepts": [ "Rationalizing the Denominator", "Simplifying Radical Products" ] } ## Identify the rationalizing factor Using the *Rationalizing the Denominator* knowledge point $$ \begin{aligned} &\text{Denominator: } \sqrt[3]{2x} = \sqrt[3]{2^1 \cdot x^1}\ &\text{To make the radicand a perfect cube, multiply by: } \sqrt[3]{2^{3-1} \cdot x^{3-1}} = \sqrt[3]{2^2 \cdot x^2} = \sqrt[3]{4x^2} \end{aligned} $$ ## Simplify the expression Using the *Rationalizing the Denominator* knowledge point $$ \begin{aligned} \frac{\sqrt[3]{3}}{\sqrt[3]{2x}} \cdot \frac{\sqrt[3]{4x^2}}{\sqrt[3]{4x^2}} &= \frac{\sqrt[3]{3 \cdot 4x^2}}{\sqrt[3]{2x \cdot 4x^2}} \ &= \frac{\sqrt[3]{12x^2}}{\sqrt[3]{8x^3}} \ &= \frac{\sqrt[3]{12x^2}}{2x} \end{aligned} $$ ## Question 1 (A) $\sqrt[3]{x^2}$

(B) $\sqrt[3]{4x}$

(C) $\sqrt[3]{4x^2}$

(D) $\sqrt[3]{2x}$ ## Question 2 (A) $\frac{\sqrt[3]{12x^2}}{2x}$

(B) $\frac{\sqrt[3]{6x}}{2x}$

(C) $\frac{\sqrt[3]{3}}{2x}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the rationalizing factor

Simplify the expression

Answer:

Question 1

Question 2