We are asked to simplify the expression:

$-3\sqrt{2} + 2\sqrt{32}$

Step 1: Simplify $\sqrt{32}$

We know that $32 = 16 \times 2$, so we can rewrite $\sqrt{32}$ as:

$\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$

Step 2: Substitute and simplify the expression

Now, substitute $4\sqrt{2}$ for $\sqrt{32}$ in the original expression:

$-3\sqrt{2} + 2(4\sqrt{2}) = -3\sqrt{2} + 8\sqrt{2}$

Step 3: Combine like terms

Both terms involve $\sqrt{2}$, so we can combine them:

$-3\sqrt{2} + 8\sqrt{2} = (8 - 3)\sqrt{2} = 5\sqrt{2}$

Final Answer:

The simplified expression is:

$5\sqrt{2}$

Would you like further explanation on this, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. How do you simplify expressions involving cube roots, such as $\sqrt[3]{27}$?
2. What is the process for simplifying square roots that involve variables?
3. Can you explain how to add or subtract different types of radicals, like cube roots or higher powers?
4. How do you deal with nested square roots in expressions?
5. How can you check if a radical expression is in its simplest form?

Tip: When simplifying square roots, always look for perfect squares (like 4, 9, 16, etc.) to factor out of the radicand.