1. **State the problem:** Simplify the expression $14 \times 3\sqrt{5} \times \sqrt{15}$. 2. **Recall the rules:** The product of square roots can be combined as $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$. Also, multiplication is associative and commutative, so we can rearrange terms. 3. **Combine the square roots:** $$3\sqrt{5} \times \sqrt{15} = 3 \times \sqrt{5 \times 15} = 3 \times \sqrt{75}$$ 4. **Simplify $\sqrt{75}$:** $$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$$ 5. **Substitute back:** $$3 \times \sqrt{75} = 3 \times 5\sqrt{3} = 15\sqrt{3}$$ 6. **Multiply by 14:** $$14 \times 15\sqrt{3} = 210\sqrt{3}$$ **Final answer:** $$\boxed{210\sqrt{3}}$$