simplify the following radical expression.

$\sqrt3{320}$

a.) $4\sqrt3{5}$

b.) $8\sqrt3{5}$

c.) cannot be simplified further

d.) $3\sqrt3{10}$

Question

simplify the following radical expression.

$\sqrt3{320}$

a.) $4\sqrt3{5}$

b.) $8\sqrt3{5}$

c.) cannot be simplified further

d.) $3\sqrt3{10}$

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": [ "Radical Properties" ], "new_concepts": [ "Simplifying Cube Roots" ], "current_concepts": [ "Radical Properties", "Simplifying Cube Roots" ] } ## Find the largest perfect cube factor of 320 Using the *Radical Properties* knowledge point $$ \begin{aligned} 320 &= 64 \times 5 \ 64 &= 4^3 \end{aligned} $$ ## Simplify the radical expression Using the *Radical Properties* knowledge point $$ \begin{aligned} \sqrt[3]{320} &= \sqrt[3]{64 \times 5} \ &= \sqrt[3]{64} \times \sqrt[3]{5} \ &= 4\sqrt[3]{5} \end{aligned} $$

a.) $4\sqrt[3]{5}$

b.) $8\sqrt[3]{5}$

c.) Cannot be simplified further

d.) $3\sqrt[3]{10}$

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

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QUESTION IMAGE

Question

Explanation:

Find the largest perfect cube factor of 320

Simplify the radical expression

Answer: