[tex]6. \\a) \\4\sqrt{5}+2\sqrt{5}=6\sqrt5\\\\b)\\\sqrt{15}*\sqrt{1\frac23}=\sqrt{15}*\sqrt{\frac53}=\sqrt{15*\frac53}=\sqrt{5*5}=\sqrt{25}=5\\\\c) \\\sqrt{300}-6\sqrt{3}=\sqrt{100*3}-6\sqrt{3}=10\sqrt3-6\sqrt3=4\sqrt3\\\\d)\\2\sqrt{10}*\frac15\sqrt5=2\sqrt{5*2}*\frac15\sqrt5=2\sqrt5*\sqrt2*\frac15\sqrt5=\frac25\sqrt{5*5*2}=\frac25\sqrt{25*2}=\frac25*5\sqrt2=2\sqrt2[/tex]
[tex]e)\\(\frac{5\sqrt6}{2})^2=\frac{(5\sqrt6)^2}{2^2}=\frac{25*6}{4}=\frac{150}{4}=37\frac24=37\frac12[/tex]
