Let's simplify the given expression:

$-2\sqrt{8} + 3\sqrt{8}$

Step 1: Factor the square root

We know that:

$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

Substituting this into the expression:

$-2(2\sqrt{2}) + 3(2\sqrt{2})$

Step 2: Multiply the coefficients

$-4\sqrt{2} + 6\sqrt{2}$

Step 3: Combine like terms

$(6 - 4)\sqrt{2} = 2\sqrt{2}$

Final Answer:

$\mathbf{2\sqrt{2}}$

Would you like a step-by-step breakdown of any part?

Here are some related questions you might find useful:

1. How do you simplify radical expressions with different radicands?
2. What are the properties of square roots that help in simplification?
3. How do you factor square roots for different numbers?
4. Can this technique be applied to cube roots or higher radicals?
5. How does this concept help in solving algebraic equations?

Tip: Always look for perfect squares inside a square root to simplify radical expressions easily!