Let's simplify the expression $6\sqrt{2} + 2\sqrt{8}$.

1. First, simplify $2\sqrt{8}$. We know that $\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$. So, $2\sqrt{8} = 2 \times 2\sqrt{2} = 4\sqrt{2}$

2. Now, substitute this back into the original expression: $6\sqrt{2} + 4\sqrt{2}$

3. Since both terms involve $\sqrt{2}$, we can combine them: $(6 + 4)\sqrt{2} = 10\sqrt{2}$

So, the simplified expression is $\boxed{10\sqrt{2}}$.

Would you like a more detailed explanation or have any questions about the solution? Here are some related questions:

1. How do we simplify square roots like $\sqrt{18}$?
2. Can we simplify expressions with cube roots in a similar way?
3. What is the difference between rationalizing and simplifying square roots?
4. How do you combine square roots with different radicands (e.g., $\sqrt{2} + \sqrt{3}$)?
5. How do you simplify a sum of square roots in higher powers (e.g., $\sqrt{16} + \sqrt{64}$)?

Tip: Always look for ways to break down square roots into smaller, familiar parts to simplify them, especially when they involve factors of perfect squares.