Let's solve the expression:

\[
\sqrt{8} \times (2\sqrt{2} - 3\sqrt{3})
\]

### Step 1: Simplify \(\sqrt{8}\)
We know that \(\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}\).

So, the expression becomes:

\[
2\sqrt{2} \times (2\sqrt{2} - 3\sqrt{3})
\]

### Step 2: Distribute \(2\sqrt{2}\) across the terms in the parentheses
\[
2\sqrt{2} \times 2\sqrt{2} - 2\sqrt{2} \times 3\sqrt{3}
\]

### Step 3: Simplify each term
1. \(2\sqrt{2} \times 2\sqrt{2} = 4 \times 2 = 8\)
2. \(2\sqrt{2} \times 3\sqrt{3} = 6\sqrt{6}\)

So, the expression simplifies to:

\[
8 - 6\sqrt{6}
\]

Thus, the simplified result is:

\[
\boxed{8 - 6\sqrt{6}}
\]

Would you like more details on the steps?

Here are 5 related questions you might find helpful:
1. How do you simplify square roots involving products like \(\sqrt{8}\)?
2. What is the distributive property in algebra, and how does it work with square roots?
3. How do you multiply two radical terms such as \(\sqrt{2} \times \sqrt{2}\)?
4. What is the difference between like and unlike radical terms?
5. Can radical expressions like this be further simplified in some cases?

**Tip:** Always simplify square roots before distributing or combining terms—it helps keep the calculations manageable!

Solve the expression sqrt(8) * (2sqrt(2) - 3sqrt(3)) step-by-step. Learn how to simplify radicals and apply the distributive property to get the final answer of 8 - 6sqrt(6). Ideal for students in Grades 9-11.

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