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The simplified expression of \( 2\sqrt{2} + \sqrt{8} + \sqrt{32} + 2\sqrt{3} + \sqrt{12} \) is:

\[
8\sqrt{2} + 4\sqrt{3}
\]

Would you like further details or have any questions? Here are some related questions:

1. How do you simplify square roots like \( \sqrt{8} \) or \( \sqrt{32} \)?
2. What properties of square roots were used in this simplification?
3. How can you apply this knowledge to similar problems with different numbers?
4. What would happen if there were cube roots in the expression instead?
5. How would this expression change if one of the square roots had a negative number?

**Tip:** When simplifying square roots, break the number into its prime factors to see if any perfect squares can be factored out.

Learn how to simplify the expression 2√2 + √8 + √32 + 2√3 + √12 with step-by-step instructions. This problem focuses on key concepts in algebra and simplifying square roots, suitable for students in Grades 8-10.

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