QUESTION IMAGE
Question
solve \\(x^2 = 4096\\). give only the positive root.
66
64
<pre_analysis>
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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>
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<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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],
"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>