9) \( \begin{aligned} \sqrt{18} & =\sqrt{9 \times 2} \\ & =3 \sqrt{2}\end{aligned} \)

Did you know that the process of simplifying square roots dates back to ancient civilizations? The Babylonians were among the first to use an early form of algebra, which included methods for finding square roots, about 4000 years ago! They utilized an iterative approach that resembles what we now call the "Babylonian method” for computing square roots. Imagine how they would have marveled at methods we use today! When simplifying square roots, a common mistake is to overlook negative roots. It’s critical to remember that every positive real number actually has two square roots: one positive and one negative. For instance, while \(\sqrt{18} = 3\sqrt{2}\) gives you the principal (or positive) square root, it’s also important to acknowledge that \(-3\sqrt{2}\) is a valid solution if you’re exploring equations or functions. Keep this in mind to avoid confusion in your calculations!