\begin{tabular}{l} Algebra \( 1> \) EE. 1 Simplify radical expressions ZFF \\ Simplify. \\ \( \sqrt{63} \) \\ \hline\end{tabular}

To simplify \( \sqrt{63} \), you can start by breaking it down into its prime factors. Notice that \( 63 = 9 \times 7 \), and since \( 9 \) is a perfect square, you can simplify it further: \[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3\sqrt{7}. \] Therefore, the simplified form of \( \sqrt{63} \) is \( 3\sqrt{7} \). Now, what's super cool about simplifying radicals is that it helps you see the underlying structure of numbers. For instance, every time you simplify a radical, you're not just reducing it; you're peeling back layers to see the simpler components, which often reveals patterns and connections between different numbers and their properties! Plus, knowing how to simplify roots is super handy in real-life situations like engineering, physics, or even architecture. Whenever you need to calculate areas or volumes that involve these square roots, being able to simplify them can make complex calculations much simpler and easier to understand.