Chapter 4 - Quadratic Functions and Equations - Square Roots and Radicals - Exercises - Page 225: 1

$$3\sqrt2$$

RECALL: (1) For any real numbers $a \ge 0, b\ge0$, $\sqrt{ab}=\sqrt{a} \cdot \sqrt{b}$ (2) For any real numbers $a \ge 0, b\gt 0$, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$ Note that $18=9(2)$. Thus, using rule (1) above gives: \begin{align*} \sqrt{18}&=\sqrt{9(2)}\\ &=\sqrt{9} \cdot \sqrt2\\ &=3\sqrt2 \end{align*}