select the correct answer.

which expression is equivalent to $18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}$ if $x \
eq 0$?

$\bigcirc\ 12x^4\sqrt{2}$
$\bigcirc\ 3x^4\sqrt{2}$
$\bigcirc\ 3x^4\sqrt{7}$
$\bigcirc\ 3x\sqrt{2}$

Question

select the correct answer.

which expression is equivalent to $18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}$ if $x \
eq 0$?

$\bigcirc\ 12x^4\sqrt{2}$
$\bigcirc\ 3x^4\sqrt{2}$
$\bigcirc\ 3x^4\sqrt{7}$
$\bigcirc\ 3x\sqrt{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Simplifying Radical Expressions" ], "new_concepts": [], "current_concepts": [ "Simplifying Radical Expressions", "Exponent Rules" ] } ## Simplify the radicals in the expression $$ \begin{aligned} \sqrt{14x^8} &= \sqrt{14} \cdot \sqrt{x^8} = x^4\sqrt{14} \ \sqrt{7x^4} &= \sqrt{7} \cdot \sqrt{x^4} = x^2\sqrt{7} \end{aligned} $$ ## Substitute and write as a single fraction $$ \frac{18x^2 \cdot x^4\sqrt{14}}{6 \cdot x^2\sqrt{7}} = \frac{18x^6\sqrt{14}}{6x^2\sqrt{7}} $$ ## Divide the coefficients, variables, and radicals $$ \begin{aligned} \frac{18}{6} &= 3 \ \frac{x^6}{x^2} &= x^4 \ \frac{\sqrt{14}}{\sqrt{7}} &= \sqrt{\frac{14}{7}} = \sqrt{2} \ \text{Result} &= 3x^4\sqrt{2} \end{aligned} $$

(A) $12x^4\sqrt{2}$

(B) $3x^4\sqrt{2}$

(C) $3x^4\sqrt{7}$

(D) $3x\sqrt{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Simplifying Radical Expressions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the radicals in the expression

Substitute and write as a single fraction

Divide the coefficients, variables, and radicals

Answer: