[tex]a) \ 4(\sqrt{3})^{2} = 4\cdot3 = 12\\\\b) \ (2\sqrt{2})^{2} =2^{2}\cdot(\sqrt{2})^{2} = 4\cdot2 = 8\\\\c) \ \sqrt{7}\cdot3\sqrt{7} =3\sqrt{7\cdot7} = 3\sqrt{7^{2}} = 3\cdot7 = 21\\\\d) \ 2\sqrt{3}\cdot5\sqrt{3} = 2\cdot5\sqrt{3\cdot3} = 10\cdot3 = 30\\\\e) \ (\frac{2\sqrt{5}}{5})^{2} = \frac{4\cdot5}{25} = \frac{20}{25} = \frac{4}{5}\\\\f) \ (\frac{2}3}\sqrt{6})^{2} = \frac{4}{9}\cdot6 = \frac{4}{3}\cdot2 = \frac{8}{3} = 2\frac{2}{3}[/tex]
[tex]g) \ (-0,1\sqrt{10})^{2} = (-0,1)^{2}\cdot(\sqrt{10})^{2} = 0,01\cdot10 =0,1\\\\h) \ -3\sqrt{15}\cdot2\sqrt{15} = -6\sqrt{15\cdot15} = -6\sqrt{15^{2}} = -6\cdot15 = -90[/tex]
