\(c,\sqrt{19-6\sqrt{10}}-\sqrt{19+6\sqrt{10}}\\ =\left(\sqrt{10}-3\right)-\left(\sqrt{10}+3\right)\\ =-6\\ d,\sqrt{12-6\sqrt{3}}-\sqrt{12+6\sqrt{3}}\\ =\left(3-\sqrt{3}\right)-\left(3+\sqrt{3}\right)=-2\sqrt{3}\\ e,\sqrt{30+10\sqrt{5}}-\sqrt{6-2\sqrt{5}}\\ =\left(5+\sqrt{5}\right)-\left(\sqrt{5}-1\right)\\ =6\\ f,\sqrt{9-4\sqrt{5}}+\sqrt{14-6\sqrt{5}}\\ =\left(\sqrt{5}-2\right)+\left(3-\sqrt{5}\right)=1\\ g,\sqrt{8-2\sqrt{7}}+\sqrt{23-8\sqrt{7}}\\ =\left(\sqrt{7}-1\right)+\left(4-\sqrt{7}\right)\\ =3\)
\(\sqrt{19-6\sqrt{10}}-\sqrt{19+6\sqrt{10}}=\sqrt{\left(3-\sqrt{10}\right)^2}-\sqrt{\left(3+\sqrt{10}\right)^2}=\sqrt{10}-3-3-\sqrt{10}=-6\)
