[tex]a) \ \sqrt[3]{1000}+\sqrt{16}= \sqrt[3]{10^{3}}+\sqrt{4^{2}}= 10+4=\boxed{14}[/tex]
[tex]b) \ \sqrt[3]{5^{2}+10^{2}}=\sqrt[3]{25+100}=\sqrt[3]{125}=\sqrt[3]{5^{3}}=\boxed{5}[/tex]
[tex]c) \ \sqrt{5^{2}}+\sqrt[3]{17^{3}}=5+17=\boxed{22}[/tex]
[tex]d) \ \dfrac{\sqrt{72}+\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{2}(\sqrt{36})+1}{\sqrt{2}} =\sqrt{36}+1=\sqrt{6^{2}}+1=6+1=\boxed{7}[/tex]
[tex]e) \ \sqrt[3]{2}\cdot\sqrt[3]{32}+\sqrt{2}\cdot\sqrt{8}=\sqrt[3]{64}+\sqrt{16}=\sqrt[3]{4^{3}}+\sqrt{4^{2}}=4+4=\boxed{8}[/tex]
