Сравнить. корень 1,5 и корень 1 2/3 Сократите дробь .а) 3+корень 3/корень 15+ корень 5...

Решите задачу:

$\displaystyle 1)..\sqrt{1,5}=\sqrt{\frac{15}{10}}=\sqrt{\frac{135}{90}}\\\\\sqrt{1\frac{2}{3}}=\sqrt{\frac{5}{3}}=\sqrt{\frac{15}{9}}=\sqrt{\frac{150}{90}}\\\\\\\frac{135}{90}\ \textless \ \frac{150}{90}=\ \textgreater \ \sqrt{1,5}\ \textless \ \sqrt{1\frac{2}{3}}\\\\\\2)..\\a)..\frac{3+\sqrt{3}}{\sqrt{15}+\sqrt{5}}=\frac{\sqrt{3}(\sqrt{3}+1)}{sqrt{5}(\sqrt{3}+1)}=\frac{\sqrt{3}}{\sqrt{5}}=\frac{\sqrt{15}}{5}$

$\displaystyle 3)..3\sqrt{2}+\sqrt{50}-\sqrt{18}=3\sqrt{2}+5\sqrt{2}-3\sqrt{2}=5\sqrt{2}\\\\\\4)..\\a)..\frac{1}{\sqrt{7}-\sqrt{5}}=\frac{\sqrt{7}+\sqrt{5}}{(\sqrt{7}-\sqrt{5})(\sqrt{7}+\sqrt{5})}= \frac{\sqrt{7}+\sqrt{5}}{(\sqrt{7})^{2}-(\sqrt{5})^{2}}=\\\\=\frac{\sqrt{7}+\sqrt{5}}{7-5}=\frac{\sqrt{7}+\sqrt{5}}{2}$

$\displaystyle b)..\frac{1}{\sqrt{4+2\sqrt{3}}}=\frac{\sqrt{4-2\sqrt{3}}}{(\sqrt{4+2\sqrt{3}})(\sqrt{4-2\sqrt{3}})}= \frac{\sqrt{4-2\sqrt{3}}}{\sqrt{4^{2}-4*3}}= \\ \\ = \frac{\sqrt{4-2\sqrt{3}}}{2}$