Working with Radicals

Ever wonder what all those symbols in a radical expression mean? Let's break it down: in $\sqrt[n]{b}$, the $n$ is the index (what power we're undoing), and $b$ is the radicand (the number under the radical symbol).

Radicals follow specific rules that make them easier to work with. When multiplying radicals, you can combine what's under the symbol: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$. For division, it works similarly: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$.

When you have a radical in the denominator, it's usually better to rationalize it (get rid of the radical at the bottom). Just multiply both top and bottom by the same radical: $\frac{3}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3}$.

💡 Quick Tip: When simplifying radicals like $-\sqrt{98}$, try factoring the radicand into perfect squares: $-\sqrt{98} = -\sqrt{49 \cdot 2} = -7\sqrt{2}$. This makes calculations much easier!