1. **State the problem:** Multiply the square roots $\sqrt{3}$ and $\sqrt{5}$ and write the answer in simplest form. 2. **Recall the multiplication rule for square roots:** $$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$$ This means we can multiply the numbers inside the square roots directly. 3. **Apply the rule:** $$\sqrt{3} \cdot \sqrt{5} = \sqrt{3 \times 5}$$ 4. **Multiply inside the root:** $$\sqrt{15}$$ 5. **Simplify if possible:** 15 is not a perfect square and has no perfect square factors other than 1, so $\sqrt{15}$ is already in simplest form. **Final answer:** $$\sqrt{15}$$