Let's solve the given expression step by step:

Expression:

$2\sqrt{2} + \sqrt{32}$

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: $2\sqrt{2} + 4\sqrt{2} = (2 + 4)\sqrt{2} = 6\sqrt{2}.$

Final Answer:

$6\sqrt{2}$

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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?

Tip:

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