Question

fill in the blank so that the resulting statement is true.

the square root property states that if \\(u^2 = d\\), then \\(u =\\)

options:
\\(d\\)
\\(\pm\sqrt{d}\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Solving by Radicals"
],
"new_concepts": [],
"current_concepts": [
"Solving by Radicals",
"Quadratic Equations"
]
}
</pre_analysis>

<reasoning>

State the square root property

Using the Solving by Radicals knowledge point
\[
\text{If } u^2 = d, \text{ then } u = \pm\sqrt{d}
\]
</reasoning>

<answer>
The square root property states that if \(u^2 = d\), then \(u =\)
<mcq-option>\(d\)</mcq-option>
<mcq-correct>\(\pm\sqrt{d}\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving by Radicals"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"tutor",
"mastery_adaptive_brevity"
],
"needs_drawing": false,
"concepts_used": [
"Solving by Radicals"
],
"new_concepts": [],
"current_concepts": [
"Solving by Radicals",
"Quadratic Equations"
]
}
</pre_analysis>

<reasoning>

State the square root property

Using the Solving by Radicals knowledge point
\[
\text{If } u^2 = d, \text{ then } u = \pm\sqrt{d}
\]
</reasoning>

<answer>
The square root property states that if \(u^2 = d\), then \(u =\)
<mcq-option>\(d\)</mcq-option>
<mcq-correct>\(\pm\sqrt{d}\)</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Solving by Radicals"
]
}
</post_analysis>