NAJ I DUZO PUNKTOW!!!
Zadanie w zalaczniku, z gory dziekuje bardzo!!
![NAJ I DUZO PUNKTOWZadanie W Zalaczniku Z Gory Dziekuje Bardzo class=](https://pl-static.z-dn.net/files/de6/b27ef057bfc3d6ddfaca29edff2ee888.jpg)
Odpowiedź:
[tex]a)\ \ \sqrt{3}\cdot\sqrt{\frac{5}{3}}=\sqrt{\not3^1\cdot\frac{5}{\not3_{1}}}=\sqrt{5}\\\\\\b)\ \ \dfrac{6\sqrt{5}-4\sqrt{5}}{\sqrt{5}}=\dfrac{(6-4)\sqrt{5}}{\sqrt{5}}=\dfrac{2\sqrt{\not5}}{\sqrt{\not5}}=2\\\\\\c)\ \ \dfrac{\sqrt{7}}{2\sqrt{7}+4\sqrt{7}}=\dfrac{\sqrt{7}}{(2+4)\sqrt{7}}=\dfrac{\sqrt{\not7}}{6\sqrt{\not7}}=\dfrac{1}{6}\\\\\\d)\ \ \dfrac{8\sqrt{3}-2\sqrt{3}}{4\sqrt{3}-\sqrt{3}}=\dfrac{(8-2)\sqrt{3}}{(4-1)\sqrt{3}}=\dfrac{6\sqrt{\not3}}{3\sqrt{\not3}}=\dfrac{6}{3}=2[/tex]
[tex]e)\ \ 2\sqrt{3}\cdot3\sqrt{2}=6\sqrt{3\cdot2}=6\sqrt{6}\\\\\\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{\not3}}{3\sqrt{\not3}}=\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]{3\cdot10}}{\sqrt[3]{5}}=\dfrac{-6\sqrt[3]{30}}{\sqrt[3]{5}}=-6\sqrt[3]{\frac{30}{5}}=\\\\=-6\sqrt[3]{6}[/tex]