1. **Problem 1.16:** Calculate $ (6\sqrt{5} + 2\sqrt{3}) \times 9\sqrt{5} $. 2. **Formula and rules:** Use distributive property: $ (a+b)c = ac + bc $. Also, $ \sqrt{a} \times \sqrt{b} = \sqrt{ab} $. 3. **Step-by-step:** $$ (6\sqrt{5} + 2\sqrt{3}) \times 9\sqrt{5} = 6\sqrt{5} \times 9\sqrt{5} + 2\sqrt{3} \times 9\sqrt{5} $$ $$ = 54 \times (\sqrt{5} \times \sqrt{5}) + 18 \times (\sqrt{3} \times \sqrt{5}) $$ $$ = 54 \times \sqrt{25} + 18 \times \sqrt{15} $$ $$ = 54 \times 5 + 18 \sqrt{15} = 270 + 18\sqrt{15} $$ **Final answer:** $270 + 18\sqrt{15}$