The square root of $18z^2$ can be simplified as follows:

$\sqrt{18z^2}$

Step 1: Factor the expression

$\sqrt{18z^2} = \sqrt{9 \cdot 2 \cdot z^2}$

Step 2: Apply the square root to each factor

$\sqrt{9} \cdot \sqrt{2} \cdot \sqrt{z^2}$

Since $\sqrt{9} = 3$ and $\sqrt{z^2} = z$, the expression simplifies to:

$3z\sqrt{2}$

Final Answer:

$\sqrt{18z^2} = 3z\sqrt{2}$

Would you like a step-by-step breakdown of the process?

Here are five related questions you might find useful:

1. What is the square root of $50x^4$?
2. How do you simplify square roots involving variables?
3. What are the properties of square roots that help in simplification?
4. How do you rationalize the denominator with square roots?
5. What is the principal square root of a number?

Tip: Always look for perfect square factors to simplify square roots efficiently.