To simplify the expression $4\sqrt{8} - \sqrt{32}$, we first need to simplify the square roots.

Step 1: Simplify each square root

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

Step 2: Substitute back into the original expression

$4\sqrt{8} - \sqrt{32} = 4(2\sqrt{2}) - 4\sqrt{2}$ $= 8\sqrt{2} - 4\sqrt{2}$

Step 3: Combine like terms

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

Thus, the simplified expression is $4\sqrt{2}$.

Would you like more details on any of the steps, or do you have any other questions?

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Here are 5 related questions:

1. How would you simplify $\sqrt{50} + \sqrt{18}$?
2. What is $5\sqrt{12} - 3\sqrt{27}$?
3. Can you simplify $6\sqrt{2} + 3\sqrt{8}$?
4. What happens if you have $7\sqrt{20} - 2\sqrt{5}$?
5. How would you add $9\sqrt{45} + \sqrt{5}$?

Tip: Always try to express square roots in terms of their simplest form by factoring out perfect squares.