Let's simplify the expression $\sqrt{8} + 2\sqrt{32} - 5\sqrt{2}$.

1. Simplify each square root:

   • $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$
   • $\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$
   • $\sqrt{2}$ remains as it is.

2. Substitute the simplified terms into the original expression: $2\sqrt{2} + 2 \times 4\sqrt{2} - 5\sqrt{2}$

3. Simplify further by performing the multiplications: $2\sqrt{2} + 8\sqrt{2} - 5\sqrt{2}$

4. Combine like terms:

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

So, the simplified expression is $5\sqrt{2}$.

Would you like to dive into more details, or do you have any questions?

Here are some related questions for practice:

1. Simplify the expression $3\sqrt{18} + 4\sqrt{50} - \sqrt{8}$.
2. What is the value of $7\sqrt{2} + 3\sqrt{18} - 2\sqrt{50}$?
3. Simplify $4\sqrt{12} - 3\sqrt{27} + 2\sqrt{75}$.
4. Evaluate $\sqrt{72} + 2\sqrt{32} - 3\sqrt{50}$.
5. Simplify the expression $6\sqrt{20} - 4\sqrt{45} + 5\sqrt{5}$.

Tip: When simplifying square roots, always look for perfect square factors to reduce the expression.