Let’s simplify the given expression step-by-step:

Given:
$\sqrt{\left(8(4902) - 36864\right) \left(8(47094) - 369664\right)}$

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Step 1: Evaluate the expressions inside the parentheses

1. For the first part:
   $8 \cdot 4902 = 39216$
   $39216 - 36864 = 2352$

2. For the second part:
   $8 \cdot 47094 = 376752$
   $376752 - 369664 = 7088$

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Step 2: Substitute these results into the square root expression

$\sqrt{2352 \cdot 7088}$

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Step 3: Simplify the product inside the square root

$2352 \cdot 7088 = 16643040$

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Step 4: Take the square root

$\sqrt{16643040} = 4080$

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Final Answer

$\boxed{4080}$

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Do you have any questions or need more details?

Here are 5 related questions you might find useful:

1. What are the steps to simplify complex square roots?
2. How can we factor large numbers efficiently?
3. What are some applications of expressions with nested square roots?
4. How can we use properties of radicals to solve similar problems?
5. What are alternative ways to estimate large square roots?

Tip: Always double-check intermediate arithmetic steps to avoid small calculation errors!