[tex]4\sqrt5+2\sqrt5=6\sqrt5\\\\\sqrt{15}-\sqrt{1\frac23}=\sqrt{15}-\sqrt{\frac53}=\sqrt{15}-\sqrt{\frac{15}9}=\sqrt{15}-\dfrac{\sqrt{15}}3=\sqrt{15}-\frac13\sqrt{15}=\\\\{}\qquad\qquad\qquad\qquad\qquad\qquad \qquad\qquad \qquad\qquad\qquad\qquad\qquad\qquad\ =\frac23\sqrt{15}\\\\ \sqrt{300}-6\sqrt3=\sqrt{100\cdot3}-6\sqrt3=\sqrt{100}\cdot\sqrt3-6\sqrt3=10\sqrt3-6\sqrt3=4\sqrt3\\\\ 2\sqrt{10}\cdot\frac15\sqrt5= \frac25\sqrt{50}=\frac25\sqrt{25\cdot2}=\frac25\sqrt{25}\cdot\sqrt2=\frac25\cdot5\sqrt2=2\sqrt2[/tex]
