evaluate the following radical.

$\sqrt{-36}$

a.) non-real solution
b.) 6
c.) -18
d.) -6

Question

evaluate the following radical.

$\sqrt{-36}$

a.) non-real solution
b.) 6
c.) -18
d.) -6

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perfect Squares", "Square Roots", "Radical Properties" ], "new_concepts": [ "Complex Numbers Introduction" ], "current_concepts": [ "Perfect Squares", "Square Roots", "Radical Properties", "Complex Numbers Introduction" ] } ## Identify the given expression $$ \sqrt{-36} $$ ## Analyze the domain of real square roots $$ \begin{aligned} &\text{For any real number } x, \sqrt{x} \text{ is real if and only if } x \ge 0.\ &\text{Here, } x = -36 < 0. \end{aligned} $$ ## Determine the solution type $$ \sqrt{-36} otin \mathbb{R} \implies \text{Non-real solution} $$

a.) Non-real solution

b.) 6

c.) -18

d.) -6

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

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QUESTION IMAGE

Question

Explanation:

Identify the given expression

Analyze the domain of real square roots

Determine the solution type

Answer: