1. **Problem:** Calculate the products and simplify the radicals as requested. 2. **Step a) Calculate $\sqrt{7} \times \sqrt{8}$:** - Use the property $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$. - So, $\sqrt{7} \times \sqrt{8} = \sqrt{7 \times 8} = \sqrt{56}$. - Simplify $\sqrt{56}$ by factoring 56 into $7 \times 8$ or $4 \times 14$. - Since $4$ is a perfect square, $\sqrt{56} = \sqrt{4 \times 14} = \sqrt{4} \times \sqrt{14} = 2\sqrt{14}$. 3. **Step d) Calculate $2\sqrt{5} \times 3\sqrt{2}$:** - Multiply coefficients: $2 \times 3 = 6$. - Multiply radicals: $\sqrt{5} \times \sqrt{2} = \sqrt{10}$. - So, $2\sqrt{5} \times 3\sqrt{2} = 6\sqrt{10}$. **Final answers:** - a) $2\sqrt{14}$ - d) $6\sqrt{10}$