1.
[tex]3\sqrt{8}-\sqrt{50}+7\sqrt{72} = 3\sqrt{4\cdot2}-\sqrt{25\cdot2} + 7\sqrt{72} = 3\cdot\sqrt{4}\cdot\sqrt{2} -\sqrt{25}\cdot\sqrt{2}+7\cdot\sqrt{36}\cdot\sqrt{2} =\\=3\cdot2\cdot\sqrt{2}-5\cdot\sqrt{2}+7\cdot6\cdot\sqrt{2} = 6\sqrt{2}-5\sqrt{2}+42\sqrt{2} = 43\sqrt{2}[/tex]
[tex](3\sqrt[3]{3}-1)(1-\sqrt[3]{3}) = 3\sqrt[3]{3}\cdot1-3\sqrt[3]{3}\cdot\sqrt[3]{3}-1\cdot1 -1\cdot(-\sqrt[3]{3})=3\sqrt[3]{3}-3\sqrt[3]{3\cdot3} -1+\sqrt[3]{3}=\\\\=4\sqrt[3]{3}-3\sqrt[3]{9}-1[/tex]
[tex]\frac{3\sqrt{2}}{\sqrt{3}} = \frac{3\sqrt{2}}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{2\cdot3}}{3} = \sqrt{6}[/tex]
[tex]\frac{\sqrt[3]{81}+\sqrt[3]{24}}{\sqrt[3]{3}} = \frac{\sqrt[3]{27\cdot3}+\sqrt[3]{8\cdot3}}{\sqrt[3]{3}} = \frac{\sqrt[3]{27}\cdot\sqrt[3]{3}+\sqrt[3]{8}\cdot\sqrt[3]{3}}{\sqrt[3]{3}}=\frac{3\sqrt[3]{3}+2\sqrt[3]{3}}{\sqrt[3]{3}}= \frac{5\sqrt[3]{3}}{\sqrt[3]{3}} = 5[/tex]
2.
[tex]L =\sqrt{12}\times\sqrt[3]{4} = \sqrt{4\times3}\times\sqrt[3]{4} = \sqrt{4}\times\sqrt{3}\times\sqrt[3]{4} = \sqrt{3}\times2\sqrt[3]{4} = \sqrt{3}\times\sqrt[3]{2^{3}\times4}=\\\\=\sqrt{3}\times\sqrt[3]{8\times4} = \sqrt{3}\times\sqrt[3]{32} = P[/tex]
