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simplify the following expression by combining like radicals. \\11\\sqr…

Question

simplify the following expression by combining like radicals.

\\11\sqrt{5} - \sqrt{80}\\

\\?\sqrt{\quad}\\

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Simplifying Radicals",
"Combining Like Radicals"
],
"new_concepts": [],
"current_concepts": [
"Simplifying Radicals",
"Combining Like Radicals"
]
}
</pre_analysis>

<reasoning>

Simplify the second radical

\[
\sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}
\]

Subtract the simplified terms

\[
11\sqrt{5} - 4\sqrt{5} = (11 - 4)\sqrt{5} = 7\sqrt{5}
\]
</reasoning>

<answer>
Simplify the following expression by combining like radicals.

\(11\sqrt{5} - \sqrt{80}\)

<blank>\(7\sqrt{5}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Simplifying Radicals"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Simplifying Radicals",
"Combining Like Radicals"
],
"new_concepts": [],
"current_concepts": [
"Simplifying Radicals",
"Combining Like Radicals"
]
}
</pre_analysis>

<reasoning>

Simplify the second radical

\[
\sqrt{80} = \sqrt{16 \times 5} = 4\sqrt{5}
\]

Subtract the simplified terms

\[
11\sqrt{5} - 4\sqrt{5} = (11 - 4)\sqrt{5} = 7\sqrt{5}
\]
</reasoning>

<answer>
Simplify the following expression by combining like radicals.

\(11\sqrt{5} - \sqrt{80}\)

<blank>\(7\sqrt{5}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Simplifying Radicals"
]
}
</post_analysis>