the area of a square is $64n^{36}$ square units. what is the side length of one side of the square?

* $8n^6$ units
* $8n^{18}$ units
* $64n^6$ units
* $64n^{18}$ units

Question

the area of a square is $64n^{36}$ square units. what is the side length of one side of the square?

* $8n^6$ units
* $8n^{18}$ units
* $64n^6$ units
* $64n^{18}$ units

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": [ "Exponent Rules", "Power of a Product" ], "new_concepts": [ "Square Root of Monomials" ], "current_concepts": [ "Exponent Rules", "Power of a Product", "Square Root of Monomials" ] } ## Set up the area equation Using the **Exponent Rules** and **Power of a Product** knowledge points $$ \begin{aligned} &s^2 = 64n^{36}\ &s = \sqrt{64n^{36}} \end{aligned} $$ ## Simplify the square root Using the **Power of a Product** knowledge point $$ \begin{aligned} &s = \sqrt{64} \cdot \sqrt{n^{36}}\ &s = 8 \cdot \sqrt{n^{36}} \end{aligned} $$ ## Apply exponent rules to the variable Using the **Exponent Rules** knowledge point $$ \begin{aligned} &\sqrt{n^{36}} = (n^{36})^{\frac{1}{2}} = n^{36 \cdot \frac{1}{2}} = n^{18}\ &s = 8n^{18} \end{aligned} $$

(A) $8n^6$ units

(B) $8n^{18}$ units

(C) $64n^6$ units

(D) $64n^{18}$ units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponent Rules" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the area equation

Simplify the square root

Apply exponent rules to the variable

Answer: