To simplify the expression \( \sqrt{22} \cdot 3 + \sqrt{322} + \sqrt{22} \), let's break it down step-by-step.
First, we rewrite the expression clearly:
\[ \sqrt{22} \cdot 3 + \sqrt{322} + \sqrt{22} \]
This can be simplified to:
\[ 3\sqrt{22} + \sqrt{322} + \sqrt{22} \]
Now, we can combine the terms involving \( \sqrt{22} \):
\[ (3\sqrt{22} + 1\sqrt{22}) + \sqrt{322} = 4\sqrt{22} + \sqrt{322} \]
Next, we simplify \( \sqrt{322} \):
\[ \sqrt{322} = \sqrt{2 \cdot 161} = \sqrt{2} \cdot \sqrt{161} \]
However, since \( \sqrt{322} \) cannot be simplified further without a calculator, we will leave it as it is.
Putting it all together, the final expression is:
\[ 4\sqrt{22} + \sqrt{322} \]
This does not match any of the exact options given, but can be represented in the closest similar form. Assuming any needed switch of notations should not affect the values matched, also note square root indexing and further computational detail might play in recognizing \( \sqrt{22} \) and its obtained values deep in expression.
Please verify if this aligns closely with what you needed to translate the provided responses concisely.
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