1. **State the problem:** Find the product of $\sqrt{66}$ and $\sqrt{15}$ in simplest radical form. 2. **Recall the property of square roots:** The product of square roots can be combined as $$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \times b}$$ 3. **Apply the property:** $$\sqrt{66} \cdot \sqrt{15} = \sqrt{66 \times 15}$$ 4. **Multiply inside the radical:** $$66 \times 15 = 990$$ So, $$\sqrt{66} \cdot \sqrt{15} = \sqrt{990}$$ 5. **Simplify $\sqrt{990}$ by factoring 990 into prime factors:** $$990 = 2 \times 3^2 \times 5 \times 11$$ 6. **Extract perfect squares from under the radical:** $$\sqrt{990} = \sqrt{2 \times \cancel{3^2} \times 5 \times 11} = 3 \sqrt{2 \times 5 \times 11}$$ 7. **Multiply the remaining factors inside the radical:** $$3 \sqrt{110}$$ **Final answer:** $$\boxed{3 \sqrt{110}}$$