The expression from the image appears to be:

$8\sqrt{5} - 4\sqrt{8} + \sqrt{32}$

Let's simplify it step-by-step:

Step 1: Simplify the square roots

• $\sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2}$
• $\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}$

Substituting back:

$8\sqrt{5} - 4(2\sqrt{2}) + 4\sqrt{2}$

Step 2: Simplify the coefficients

• $4(2\sqrt{2}) = 8\sqrt{2}$

Now the expression becomes: $8\sqrt{5} - 8\sqrt{2} + 4\sqrt{2}$

Step 3: Combine like terms

• Combine $-8\sqrt{2} + 4\sqrt{2}$: This equals $-4\sqrt{2}$.

Final simplified expression: $8\sqrt{5} - 4\sqrt{2}$

Let me know if you would like further details! Here are five related questions:

1. How can square roots be simplified in general?
2. What is the importance of combining like terms in expressions?
3. How would the simplification change if different coefficients were used?
4. Can this expression be approximated numerically? What are its decimal values?
5. How does simplifying square roots apply to solving equations?

Tip: Always check for perfect square factors in square roots for faster simplifications.