Let's simplify the expression step by step:

Given:

$4\sqrt{32} \cdot \sqrt{4}$

Step 1: Simplify $\sqrt{32}$

We can simplify $\sqrt{32}$ as follows: $\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}$

Step 2: Simplify $\sqrt{4}$

$\sqrt{4} = 2$

Step 3: Substitute the simplified expressions back into the equation

$4\sqrt{32} \cdot \sqrt{4} = 4(4\sqrt{2}) \cdot 2 = 16\sqrt{2} \cdot 2 = 32\sqrt{2}$

Thus, the simplified expression is: $32\sqrt{2}$

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:

1. Simplify $3\sqrt{18} \cdot \sqrt{9}$
2. Solve $5\sqrt{50} \cdot \sqrt{2}$
3. Simplify $\sqrt{72} \cdot \sqrt{8}$
4. What is the value of $6\sqrt{27} \cdot \sqrt{3}$?
5. Simplify $\sqrt{12} \cdot 2\sqrt{3}$

Tip: When simplifying square roots, try to factor out perfect squares to make the expression easier to handle.