Question

simplify the following expression by combining like radicals.

\\14\sqrt{7} - \sqrt{175}\\

\\?\sqrt{\quad}\\

Explanation:

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<reasoning>

Simplify the second radical term

\[
\sqrt{175} = \sqrt{25 \times 7} = \sqrt{25} \times \sqrt{7} = 5\sqrt{7}
\]

Combine the like radical terms

\[
14\sqrt{7} - 5\sqrt{7} = (14 - 5)\sqrt{7} = 9\sqrt{7}
\]
</reasoning>

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

\(14\sqrt{7} - \sqrt{175}\)

<blank>\(9\sqrt{7}\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
"Algebra",
"Simplifying Radicals"
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Answer:

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</pre_analysis>

<reasoning>

Simplify the second radical term

\[
\sqrt{175} = \sqrt{25 \times 7} = \sqrt{25} \times \sqrt{7} = 5\sqrt{7}
\]

Combine the like radical terms

\[
14\sqrt{7} - 5\sqrt{7} = (14 - 5)\sqrt{7} = 9\sqrt{7}
\]
</reasoning>

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

\(14\sqrt{7} - \sqrt{175}\)

<blank>\(9\sqrt{7}\)</blank>
</answer>

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"Mathematics",
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