Use the product rule to simplify the radical, sqrt (18) sqrt (18)= square (Simplify your answer. Type an exact answer, using radicals as needed.)

To simplify the radical \( \sqrt{18} \) using the product rule for radicals, we follow these steps:<br /><br />### Step 1: Recall the product rule for radicals<br />The product rule states:<br />\[<br />\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}<br />\]<br />We aim to break down \( 18 \) into factors where one of the factors is a perfect square.<br /><br />### Step 2: Factorize \( 18 \)<br />The number \( 18 \) can be factored as:<br />\[<br />18 = 9 \cdot 2<br />\]<br />Here, \( 9 \) is a perfect square (\( 9 = 3^2 \)).<br /><br />### Step 3: Apply the product rule<br />Using the product rule, we write:<br />\[<br />\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2}<br />\]<br /><br />### Step 4: Simplify the square root of \( 9 \)<br />Since \( \sqrt{9} = 3 \), we have:<br />\[<br />\sqrt{18} = 3 \cdot \sqrt{2}<br />\]<br /><br />### Final Answer:<br />\[<br />\sqrt{18} = 3\sqrt{2}<br />\]