to find the product of $(-2\sqrt{20k})(5\sqrt{8k^3})$, first write using a single radical. which expression is equivalent to the given product?

$-10\sqrt{160k^3}$
$-10\sqrt{160k^4}$
$3\sqrt{28k^4}$
$3\sqrt{28k^3}$

simplify $(-2\sqrt{20k})(5\sqrt{8k^3})$ completely.

$-10k^4\sqrt{16}$
$-10k^2\sqrt{16}$
$-40k^4\sqrt{10}$
$-40k^2\sqrt{10}$

Question

to find the product of $(-2\sqrt{20k})(5\sqrt{8k^3})$, first write using a single radical. which expression is equivalent to the given product?

$-10\sqrt{160k^3}$
$-10\sqrt{160k^4}$
$3\sqrt{28k^4}$
$3\sqrt{28k^3}$

simplify $(-2\sqrt{20k})(5\sqrt{8k^3})$ completely.

$-10k^4\sqrt{16}$
$-10k^2\sqrt{16}$
$-40k^4\sqrt{10}$
$-40k^2\sqrt{10}$

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": [ "Product Property of Radicals", "Radical Simplification" ], "new_concepts": [], "current_concepts": [ "Product Property of Radicals", "Radical Simplification" ] } ## Express as a single radical Using the *Product Property of Radicals* knowledge point $$ \begin{aligned} (-2\sqrt{20k})(5\sqrt{8k^3}) &= (-2 \cdot 5) \cdot \sqrt{20k \cdot 8k^3} \ &= -10\sqrt{160k^4} \end{aligned} $$ ## Simplify the expression completely Using the *Radical Simplification* knowledge point $$ \begin{aligned} -10\sqrt{160k^4} &= -10\sqrt{16 \cdot 10 \cdot (k^2)^2} \ &= -10 \cdot 4k^2\sqrt{10} \ &= -40k^2\sqrt{10} \end{aligned} $$ ## Question 1 (A) $-10\sqrt{160k^3}$

(B) $-10\sqrt{160k^4}$

(C) $3\sqrt{28k^4}$

(D) $3\sqrt{28k^3}$ ## Question 2 (A) $-10k^4\sqrt{16}$

(B) $-10k^2\sqrt{16}$

(C) $-40k^4\sqrt{10}$

(D) $-40k^2\sqrt{10}$

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

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QUESTION IMAGE

Question

Explanation:

Express as a single radical

Simplify the expression completely

Answer:

Question 1

Question 2