Question

simplify the following expression by combining like radicals.

\\2\sqrt{216} + 7\sqrt{6}\\

\\?\sqrt{\quad}\\

Explanation:

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<reasoning>

Simplify the first radical term

\[

$$\begin{aligned} 2\sqrt{216} &= 2\sqrt{36 \times 6} \\ &= 2 \times 6\sqrt{6} \\ &= 12\sqrt{6} \end{aligned}$$

\]

Combine the like radical terms

\[

$$\begin{aligned} 12\sqrt{6} + 7\sqrt{6} &= (12 + 7)\sqrt{6} \\ &= 19\sqrt{6} \end{aligned}$$

\]
</reasoning>

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

\(2\sqrt{216} + 7\sqrt{6}\)

<blank>\(19\sqrt{6}\)</blank>
</answer>

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Answer:

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<reasoning>

Simplify the first radical term

\[

$$\begin{aligned} 2\sqrt{216} &= 2\sqrt{36 \times 6} \\ &= 2 \times 6\sqrt{6} \\ &= 12\sqrt{6} \end{aligned}$$

\]

Combine the like radical terms

\[

$$\begin{aligned} 12\sqrt{6} + 7\sqrt{6} &= (12 + 7)\sqrt{6} \\ &= 19\sqrt{6} \end{aligned}$$

\]
</reasoning>

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

\(2\sqrt{216} + 7\sqrt{6}\)

<blank>\(19\sqrt{6}\)</blank>
</answer>

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