1. **State the problem:** Simplify the square roots $\sqrt{108}$ and $\sqrt{180}$. 2. **Recall the rule:** To simplify $\sqrt{a}$, find the largest perfect square factor of $a$ and use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. 3. **Simplify $\sqrt{108}$:** - Factor 108: $108 = 36 \times 3$ - Since 36 is a perfect square, $\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3}$. 4. **Simplify $\sqrt{180}$:** - Factor 180: $180 = 36 \times 5$ - Since 36 is a perfect square, $\sqrt{180} = \sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5} = 6\sqrt{5}$. **Final answers:** $$\sqrt{108} = 6\sqrt{3}$$ $$\sqrt{180} = 6\sqrt{5}$$