what is the square root of $-16$?

$\bigcirc$ $-8i$
$\bigcirc$ $-4i$
$\bigcirc$ $4i$
$\bigcirc$ $8i$

Question

what is the square root of $-16$?

$\bigcirc$ $-8i$
$\bigcirc$ $-4i$
$\bigcirc$ $4i$
$\bigcirc$ $8i$

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", "Square Roots of Negative Numbers" ] } ## Express the square root of a negative number using the imaginary unit $$ \sqrt{-16} = \sqrt{16 \times (-1)} = \sqrt{16} \times \sqrt{-1} $$ ## Simplify the expression using the definition of i $$ \sqrt{16} = 4 \quad \text{and} \quad \sqrt{-1} = i $$ $$ \sqrt{-16} = 4i $$

(A) $-8i$

(B) $-4i$

(C) $4i$

(D) $8i$

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

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QUESTION IMAGE

Question

Explanation:

Express the square root of a negative number using the imaginary unit

Simplify the expression using the definition of i

Answer: