Simplify.

To simplify the expression \(\sqrt{72x^3z^3}\), we can break it down as follows:

1. **Factor the number:** Start by factoring \(72\):
\[
72 = 36 \times 2 = 6^2 \times 2
\]
So, we have:
\[
\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}
\]

2. **Simplify the variable parts:** Now let's simplify \(\sqrt{x^3}\) and \(\sqrt{z^3}\):
\[
\sqrt{x^3} = \sqrt{x^2 \cdot x} = \sqrt{x^2} \cdot \sqrt{x} = x\sqrt{x}
\]
Similarly for \(z\):
\[
\sqrt{z^3} = \sqrt{z^2 \cdot z} = \sqrt{z^2} \cdot \sqrt{z} = z\sqrt{z}
\]

3. **Combine everything:** Now we can put all these pieces together:
\[
\sqrt{72x^3z^3} = \sqrt{72} \cdot \sqrt{x^3} \cdot \sqrt{z^3} = (6\sqrt{2}) \cdot (x\sqrt{x}) \cdot (z\sqrt{z})
\]

4. **Final simplification:** Combine all the factors:
\[
= 6xyz \sqrt{2xz}
\]

So, the simplified form of \(\sqrt{72x^3z^3}\) is:
\[
\boxed{6xyz \sqrt{2xz}}
\]