Simplify.

To simplify the expression \(\sqrt{75yz^2}\), we need to break down the number inside the square root into its prime factors and identify any perfect squares.

First, we can factor \(75\):

\[
75 = 25 \cdot 3 = 5^2 \cdot 3
\]

So, we can rewrite the expression:

\[
\sqrt{75yz^2} = \sqrt{25 \cdot 3 \cdot y \cdot z^2}
\]

Next, we can separate the square root into the products of the square roots of its factors:

\[
\sqrt{75yz^2} = \sqrt{25} \cdot \sqrt{3} \cdot \sqrt{y} \cdot \sqrt{z^2}
\]

Now we can simplify the square roots of the perfect squares:

\[
\sqrt{25} = 5 \quad \text{and} \quad \sqrt{z^2} = z
\]

Substituting these back into our expression, we get:

\[
\sqrt{75yz^2} = 5 \cdot z \cdot \sqrt{3} \cdot \sqrt{y}
\]

This simplifies to:

\[
5z\sqrt{3y}
\]

Thus, the simplified expression is:

\[
\sqrt{75yz^2} = 5z\sqrt{3y}
\]