Question

simplify the radical expression by rationalizing the denominator.

\\\sqrt{\frac{50}{12}}\\

\\\frac{?\sqrt{\quad}}{\quad}\\

give your answer in simplest form.

Explanation:

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<reasoning>

Simplify the fraction inside the radical

\[
\frac{50}{12} = \frac{25}{6}
\]

Apply the quotient property of radicals

\[
\sqrt{\frac{25}{6}} = \frac{\sqrt{25}}{\sqrt{6}} = \frac{5}{\sqrt{6}}
\]

Rationalize the denominator

\[
\frac{5}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}} = \frac{5\sqrt{6}}{6}
\]
</reasoning>

<answer>
Simplify the radical expression by rationalizing the denominator.
\[\sqrt{\frac{50}{12}}\]
Give your answer in simplest form.
<blank>\(\frac{5\sqrt{6}}{6}\)</blank>
</answer>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
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"Radical Expressions"
]
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Answer:

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<reasoning>

Simplify the fraction inside the radical

\[
\frac{50}{12} = \frac{25}{6}
\]

Apply the quotient property of radicals

\[
\sqrt{\frac{25}{6}} = \frac{\sqrt{25}}{\sqrt{6}} = \frac{5}{\sqrt{6}}
\]

Rationalize the denominator

\[
\frac{5}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}} = \frac{5\sqrt{6}}{6}
\]
</reasoning>

<answer>
Simplify the radical expression by rationalizing the denominator.
\[\sqrt{\frac{50}{12}}\]
Give your answer in simplest form.
<blank>\(\frac{5\sqrt{6}}{6}\)</blank>
</answer>

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