$a)2\sqrt{5}+3\sqrt{5}=\left(2+3\right)\sqrt{5}=5\sqrt{5}$

$b)3\sqrt{7}\cdot 8=24\sqrt{7}$

$c)6\sqrt{5}\cdot \frac{1}{2}\sqrt{5}=6\cdot \frac{1}{2}\cdot \sqrt{5}\cdot \sqrt{5}=\frac{6}{2}\cdot 5=3\cdot 5=15$ $c)6\sqrt{5}\cdot \frac{1}{2}\sqrt{5}=6\cdot \frac{1}{2}\cdot \sqrt{5}\cdot \sqrt{5}=\frac{6}{2}\cdot 5=3\cdot 5=15$

$d){\left(2\sqrt{3}\right)}^2=2\sqrt{3}\cdot 2\sqrt{3}=2\cdot 2\cdot \sqrt{3}\cdot \sqrt{3}=2\cdot 2\cdot 3=4\cdot 3=12$

$e){\left(\frac{2\sqrt{6}}{3}\right)}^2=\frac{2\sqrt{6}}{3}\cdot \frac{2\sqrt{6}}{3}=\frac{2\sqrt{6}\cdot 2\sqrt{6}}{3\cdot 3}=\frac{2\cdot 2\cdot 6}{3\cdot 3}=\frac{2\cdot 2\cdot 2}{3}=\frac{8}{3}$

$f)\frac{3\sqrt{3}+0,5\sqrt{3}}{5}=\frac{3,5\sqrt{3}}{5}=3,5\sqrt{3}:5=0,7\sqrt{3}$

$g)5\sqrt[3]{7}-2,5\sqrt[3]{7}=\left(5-2,5\right)\sqrt[3]{7}=2,5\sqrt[3]{7}$

$h)2\sqrt[3]{10}-\sqrt[3]{-10}=2\sqrt[3]{10}-\sqrt[3]{-1\cdot 10}=2\sqrt[3]{10}-\sqrt[3]{-1}\cdot \sqrt[3]{10}=2\sqrt[3]{10}-\left(-1\right)\sqrt[3]{10}=2\sqrt[3]{10}+\sqrt[3]{10}=\left(2+1\right)\sqrt[3]{10}=3\sqrt[3]{10}$

$i){\left(2\sqrt[3]{-5}\right)}^3=2^3\cdot {\left(\sqrt[3]{-5}\right)}^3=8\cdot \left(-5\right)=-40$