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solve \\(x^2 = 4096\\). give only the positive root. 66 64

Question

solve \\(x^2 = 4096\\). give only the positive root.

66

64

Explanation:

Response

<pre_analysis>
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"concepts_used": [
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],
"new_concepts": [],
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</pre_analysis>

<reasoning>

Set up the quadratic equation

\[
x^2 = 4096
\]

Apply the square root property

\[
x = \pm\sqrt{4096}
\]

Calculate the positive root

\[
x = 64 \quad (\text{since } 64 \times 64 = 4096)
\]
</reasoning>

<answer>
<mcq-option>(A) 66</mcq-option>
<mcq-correct>(B) 64</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Quadratic Equations"
],
"new_concepts": [],
"current_concepts": [
"Quadratic Equations",
"Square Root Function"
]
}
</pre_analysis>

<reasoning>

Set up the quadratic equation

\[
x^2 = 4096
\]

Apply the square root property

\[
x = \pm\sqrt{4096}
\]

Calculate the positive root

\[
x = 64 \quad (\text{since } 64 \times 64 = 4096)
\]
</reasoning>

<answer>
<mcq-option>(A) 66</mcq-option>
<mcq-correct>(B) 64</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>