select the correct answer.

if $x 0$ and $y 0$, which expression is equivalent to $\sqrt{768x^{19}y^{37}}$?

$\bigcirc\ 16x^9y^{18}\sqrt{3xy}$
$\bigcirc\ 8x^4y^6\sqrt{12x^4y}$
$\bigcirc\ 16x^4y^6\sqrt{3x^4y}$
$\bigcirc\ 8x^9y^{18}\sqrt{12xy}$

Question

select the correct answer.

if $x > 0$ and $y > 0$, which expression is equivalent to $\sqrt{768x^{19}y^{37}}$?

$\bigcirc\ 16x^9y^{18}\sqrt{3xy}$
$\bigcirc\ 8x^4y^6\sqrt{12x^4y}$
$\bigcirc\ 16x^4y^6\sqrt{3x^4y}$
$\bigcirc\ 8x^9y^{18}\sqrt{12xy}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Radical Simplification", "Exponent Rules" ], "new_concepts": [], "current_concepts": [ "Radical Simplification", "Exponent Rules" ] } ## Factor the radicand into perfect squares $$ \begin{aligned} 768 &= 256 \times 3 = 16^2 \times 3 \ x^{19} &= x^{18} \times x = (x^9)^2 \times x \ y^{37} &= y^{36} \times y = (y^{18})^2 \times y \end{aligned} $$ ## Simplify the square root $$ \begin{aligned} \sqrt{768 x^{19} y^{37}} &= \sqrt{16^2 \cdot 3 \cdot (x^9)^2 \cdot x \cdot (y^{18})^2 \cdot y} \ &= 16 x^9 y^{18} \sqrt{3xy} \end{aligned} $$

(A) $16x^9y^{18}\sqrt{3xy}$

(B) $8x^4y^6\sqrt{12x^4y}$

(C) $16x^4y^6\sqrt{3x^4y}$

(D) $8x^9y^{18}\sqrt{12xy}$

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

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QUESTION IMAGE

Question

Explanation:

Factor the radicand into perfect squares

Simplify the square root

Answer: