Simplify. \[ \sqrt{18 y z^{2}} \] Assume that all variables represent positive real numbers.

To simplify \(\sqrt{18 y z^{2}}\), we first break down the square root into its factors. We can rewrite the expression under the square root: \[ \sqrt{18 y z^{2}} = \sqrt{18} \cdot \sqrt{y} \cdot \sqrt{z^{2}} \] Next, we simplify each part: 1. \(\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}\) 2. \(\sqrt{y}\) remains as \(\sqrt{y}\) 3. \(\sqrt{z^{2}} = z\) (since \(z\) is positive) Now putting it all together, we get: \[ \sqrt{18 y z^{2}} = 3\sqrt{2} \cdot \sqrt{y} \cdot z \] Thus, the simplified expression is: \[ 3z\sqrt{2y} \]