68.
a) $\sqrt{\frac{2}{3}}=\frac{\sqrt{2}}{\sqrt{3}}=\frac{\sqrt{2}\sqrt{3}}{\sqrt{3}\sqrt{3}}=\frac{\sqrt{6}}{3}$
b) $\sqrt{\frac{x^2}{5}}=\frac{\sqrt{x^2}}{\sqrt{5}}=\frac{|x|\sqrt{5}}{\sqrt{5}\sqrt{5}}=\frac{\sqrt{5}x}5{}$
c) $\sqrt{\frac{3}{x}}=\frac{\sqrt{3}}{\sqrt{x}}=\frac{\sqrt{3}\sqrt{x}}{\sqrt{x}\sqrt{x}}=\frac{\sqrt{3x}}{x}$
d) $\sqrt{x^2-\frac{x^2}{7}}=\sqrt{\frac{6x^2}{7}}=\frac{\sqrt{6x^2}}{\sqrt{7}}=\frac{\sqrt{6}x}{\sqrt{7}}=\frac{\sqrt{7}\sqrt{6}x}{\sqrt{7}\sqrt{7}}=\frac{\sqrt{42}x}{7}$
69.
a) $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{2}(\sqrt{5}-\sqrt{3})}{\sqrt{2}\sqrt{2}}=\frac{\sqrt{2}\sqrt{5}-\sqrt{2}\sqrt{3}}{2}=\frac{\sqrt{10}-\sqrt{6}}{2}$
b) $\frac{26}{5-2\sqrt{3}}=\frac{26(5+2\sqrt{3})}{(5-2\sqrt{3})(5+2\sqrt{3})}=\frac{26(5+2\sqrt{3})}{5^2-(2\sqrt{3})^2}=\frac{26(5+2\sqrt{3})}{13}=\frac{26(5+2\sqrt{3})}{13}=2(5+2\sqrt{3})=10+4\sqrt{3}$
c) $\frac{2\sqrt{10}-5}{4-\sqrt{10}}=\frac{2\sqrt{2}\sqrt{5}-\sqrt{5}\sqrt{5}}{2\sqrt{2}\sqrt{2}-\sqrt{2}\sqrt{5}}=\frac{\sqrt{5}(2\sqrt{2}-\sqrt{5})}{\sqrt{2}(2\sqrt{2}-\sqrt{5})}=\frac{\sqrt5}{\sqrt{2}}=\frac{\sqrt{5}\sqrt{2}}{\sqrt{2}\sqrt{2}}=\frac{\sqrt{10}}{2}$
d) $\frac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}=\frac{3\sqrt{3}\sqrt{3}-2\sqrt{3}}{3\sqrt{2}\sqrt{3}-2\sqrt{2}}=\frac{\sqrt{3}(3\sqrt{3}-2)}{\sqrt{2}(3\sqrt{3}-2)}=\frac{\sqrt{3}}{\sqrt{2}}=\frac{\sqrt{3}\sqrt{2}}{\sqrt{2}\sqrt{2}}=\frac{\sqrt{6}}{2}$
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