a) [tex]\sqrt{2}\cdot\sqrt{7}=\sqrt{2\cdot7}=\boxed{\sqrt{14}}\\\sqrt{3}\cdot\sqrt{10}=\sqrt{3\cdot10}=\boxed{\sqrt{30}}\\\sqrt[3]{5}\cdot\sqrt[3]{11}=\sqrt[3]{5\cdot11}=\boxed{\sqrt[3]{55}}[/tex]
b) [tex]\frac{\sqrt{10}}{\sqrt{2}}=\sqrt{\frac{10}{2}}=\boxed{\sqrt{5}}\\\\\frac{\sqrt{15}}{\sqrt{5}}=\sqrt{\frac{15}{5}}=\boxed{\sqrt{3}}\\\\\frac{\sqrt[3]{30}}{\sqrt[3]{3}}=\sqrt[3]{\frac{30}{3}}=\boxed{\sqrt[3]{10}}[/tex]
Verified answer
a) [tex]\sqrt{2}\cdot\sqrt{7}=\sqrt{2\cdot7}=\boxed{\sqrt{14}}\\\sqrt{3}\cdot\sqrt{10}=\sqrt{3\cdot10}=\boxed{\sqrt{30}}\\\sqrt[3]{5}\cdot\sqrt[3]{11}=\sqrt[3]{5\cdot11}=\boxed{\sqrt[3]{55}}[/tex]
b) [tex]\frac{\sqrt{10}}{\sqrt{2}}=\sqrt{\frac{10}{2}}=\boxed{\sqrt{5}}\\\\\frac{\sqrt{15}}{\sqrt{5}}=\sqrt{\frac{15}{5}}=\boxed{\sqrt{3}}\\\\\frac{\sqrt[3]{30}}{\sqrt[3]{3}}=\sqrt[3]{\frac{30}{3}}=\boxed{\sqrt[3]{10}}[/tex]