[tex]4.23\ \ a)\\\\ \frac{3}{\sqrt{2}}=\frac{3}{\sqrt{2}}*\frac{ \sqrt{2}}{\sqrt{2}}=\frac{3\sqrt{2}}{2}\\\\b)\\\\\frac{1}{\sqrt{3}}=\frac{1}{\sqrt{3}}*\frac{ \sqrt{3}}{\sqrt{3}}=\frac{ \sqrt{3}}{3}\\\\c)\\\\\frac{4}{3\sqrt{5}}=\frac{4}{3\sqrt{5}}*\frac{ \sqrt{5}}{\sqrt{5}}=\frac{4\sqrt{5}}{3*5}=\frac{4\sqrt{5}}{15}[/tex]
[tex]d)\\\\\frac{\sqrt{3}-\sqrt{2}}{ 5\sqrt{2}}=\frac{\sqrt{3}-\sqrt{2}}{ 5\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{(\sqrt{3}-\sqrt{2})*\sqrt{2}}{5*2}=\frac{\sqrt{6}-2}{10} \\\\e)\\\\\frac{1}{\sqrt[3]{6}}= \frac{1}{\sqrt[3]{6}}*\frac{\sqrt[3]{36}}{\sqrt[3]{36}}=\frac{\sqrt[3]{36}}{ \sqrt[3]{6*36}}=\frac{\sqrt[3]{36}}{ \sqrt[3]{6*36}}=\frac{\sqrt[3]{36}}{ \sqrt[3]{216}}=\frac{\sqrt[3]{36}}{\sqrt[3]{6^3}}=\frac{\sqrt[3]{36}}{6}\\\\f)\\\\-\frac{2}{\sqrt[4]{5}}=-\frac{2}{\sqrt[4]{5}}* \frac{ \sqrt[4]{125}}{\sqrt[4]{125}}=-\frac{2\sqrt[4]{125}}{\sqrt[4]{5*125}}=-\frac{2\sqrt[4]{125}}{\sqrt[4]{625}} =-\frac{2\sqrt[4]{125}}{\sqrt[4]{ 5^4}}=-\frac{2\sqrt[4]{125}}{5}[/tex]
[tex]g)\\\\\frac{-1}{\sqrt[5]{-2}}=\frac{-1}{\sqrt[5]{-2}}*\frac{\sqrt[5]{16}}{\sqrt[5]{16}}= \frac{-\sqrt[5]{16}}{\sqrt[5]{-2*16}}= \frac{-\sqrt[5]{16}}{\sqrt[5]{-32}}= \frac{-\sqrt[5]{16}}{\sqrt[5]{- 2^5 }}=\frac{-\sqrt[5]{16}}{-2}=\frac{ \sqrt[5]{16}}{ 2}\\\\h)\\\\ \frac{5}{\sqrt[7]{2}}= \frac{5}{\sqrt[7]{2}}* \frac{ \sqrt[7]{64}}{\sqrt[7]{64}}=\frac{5\sqrt[7]{64}}{\sqrt[7]{2*64}}=\frac{5\sqrt[7]{64}}{\sqrt[7]{128}}=\frac{5\sqrt[7]{64}}{\sqrt[7]{2^7}}=\frac{5\sqrt[7]{64}}{2}[/tex]
