which expression is equivalent to $\sqrt{-80}$?

* $-4\sqrt{5}$
* $-4i\sqrt{5}$
* $4i\sqrt{5}$
* $4\sqrt{5}$

Question

which expression is equivalent to $\sqrt{-80}$?

* $-4\sqrt{5}$
* $-4i\sqrt{5}$
* $4i\sqrt{5}$
* $4\sqrt{5}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Numbers", "Imaginary Numbers" ], "new_concepts": [], "current_concepts": [ "Complex Numbers", "Imaginary Numbers", "Simplifying Radicals" ] } ## Extract the imaginary unit $$ \sqrt{-80} = \sqrt{-1 \cdot 80} = i\sqrt{80} $$ ## Simplify the radical expression $$ \begin{aligned} i\sqrt{80} &= i\sqrt{16 \cdot 5} \ &= i \cdot 4\sqrt{5} \ &= 4i\sqrt{5} \end{aligned} $$

(A) $-4\sqrt{5}$

(B) $-4i\sqrt{5}$

(C) $4i\sqrt{5}$

(D) $4\sqrt{5}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Extract the imaginary unit

Simplify the radical expression

Answer: