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Let's solve the given expression step by step:

### Expression:
\[ 2\sqrt{2} + \sqrt{32} \]

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### Step 1: Simplify \( \sqrt{32} \)
The number 32 can be written as \( 16 \times 2 \). Using the square root property \( \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b} \), we get:
\[
\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}.
\]

So, the expression becomes:
\[
2\sqrt{2} + 4\sqrt{2}.
\]

---

### Step 2: Combine like terms
Both terms have \( \sqrt{2} \) as a common factor. Combine them:
\[
2\sqrt{2} + 4\sqrt{2} = (2 + 4)\sqrt{2} = 6\sqrt{2}.
\]

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### Final Answer:
\[
6\sqrt{2}
\]

Would you like further clarification or details about this? Let me know!  

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### Related Questions:
1. How do we simplify square roots involving larger numbers?
2. What is the difference between like and unlike radical terms?
3. Can \( \sqrt{32} \) be simplified in different ways?
4. How is the distributive property applied in simplifying radical expressions?
5. What are some common mistakes to avoid when working with square roots?

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### Tip:
When simplifying square roots, always look for the largest perfect square factor to simplify the process efficiently!

Learn how to simplify the radical expression 2√2 + √32 with a step-by-step solution. This problem involves simplifying square roots and combining like terms, applying the properties of radicals. Suitable for students in Grades 7-10.

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