Let's simplify the expression step by step:

We are given the expression:

\[
4\sqrt{27} \times 2\sqrt{32} \div \sqrt{48}
\]

### Step 1: Simplify each square root term.

1. \( \sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3} \)
2. \( \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \)
3. \( \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \)

### Step 2: Substitute the simplified square root terms back into the expression.

\[
4(3\sqrt{3}) \times 2(4\sqrt{2}) \div 4\sqrt{3}
\]

This simplifies to:

\[
12\sqrt{3} \times 8\sqrt{2} \div 4\sqrt{3}
\]

### Step 3: Simplify the division by \( 4\sqrt{3} \).

First, divide \( 12\sqrt{3} \) by \( 4\sqrt{3} \):

\[
\frac{12\sqrt{3}}{4\sqrt{3}} = 3
\]

Now the expression becomes:

\[
3 \times 8\sqrt{2} = 24\sqrt{2}
\]

### Final Answer:

\[
24\sqrt{2}
\]

Would you like a more detailed explanation or have any questions?

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Here are 5 related questions for further practice:

1. Simplify: \( 3\sqrt{50} \times 2\sqrt{18} \div \sqrt{8} \)
2. Simplify: \( 5\sqrt{20} + 3\sqrt{45} \)
3. Solve: \( \frac{\sqrt{72}}{\sqrt{18}} \)
4. Simplify: \( 7\sqrt{27} \times 2\sqrt{12} \)
5. Simplify: \( \sqrt{128} \div \sqrt{2} \)

**Tip**: When simplifying square roots, always factor the number under the root into its prime factors to identify perfect squares.

Learn how to simplify the expression 4√27 * 2√32 ÷ √48 with a step-by-step solution. This problem focuses on simplifying radicals and multiplying and dividing square roots. Ideal for students in Grades 8-10.

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