Odpowiedź:
[tex]a)\ \ \sqrt{3}\cdot\sqrt{\frac{5}{3}}=\sqrt{\not3\cdot\frac{5}{\not3}}=\sqrt{5}\\\\\\b)\ \ \dfrac{6\sqrt{5}-4\sqrt{5}}{\sqrt{5}}=\dfrac{2\sqrt{5}}{\sqrt{5}}=2\\\\\\c)\ \ \dfrac{\sqrt{7}}{2\sqrt{7}+4\sqrt{7}}=\dfrac{\sqrt{7}}{6\sqrt{7}}=\dfrac{1}{6}\\\\\\d)\ \ \dfrac{8\sqrt{3}-2\sqrt{3}}{4\sqrt{3}-\sqrt{3}}=\dfrac{6\sqrt{3}}{3\sqrt{3}}=\dfrac{6}{3}=2\\\\\\e)\ \ 2\sqrt{3}\cdot3\sqrt{2}=2\cdot3\cdot\sqrt{3\cdot2}=6\sqrt{6}[/tex]
[tex]f)\ \ \dfrac{6\sqrt{27}}{3\sqrt{3}}=\dfrac{6\sqrt{9\cdot3}}{3\sqrt{3}}=\dfrac{6\cdot3\sqrt{3}}{3\sqrt{3}}=\dfrac{18\sqrt{3}}{3\sqrt{3}}=\dfrac{18}{3}=6\\\\\\g)\ \ \dfrac{\sqrt[3]{2}\cdot\sqrt[3]{15}}{\sqrt[3]{6}}=\dfrac{\sqrt[3]{2\cdot15}}{\sqrt[3]{6}}=\dfrac{\sqrt[3]{30}}{\sqrt[3]{6}}=\sqrt[3]{\frac{30}{6}}=\sqrt[3]{5}[/tex]
[tex]h)\ \ \dfrac{2\sqrt[3]{3}\cdot3\sqrt[3]{-10}}{\sqrt[3]{5}}=\dfrac{2\sqrt[3]{3}\cdot3\cdot(-\sqrt[3]{10})}{\sqrt[3]{5}}=\dfrac{-6\sqrt[3]{30}}{\sqrt[3]{5}}=-6\sqrt[3]{\frac{30}{5}}=-6\sqrt[3]{6}[/tex]
