\(\sqrt{2}\left(2\sqrt{8}+3\sqrt{32}-4\sqrt{50}\right)=\sqrt{2}\left(4\sqrt{2}+12\sqrt{2}-20\sqrt{2}\right)=\sqrt{2}.\left(-4\sqrt{2}\right)=-8\)
\(\sqrt{3\sqrt{2}-2\sqrt{3}}.\sqrt{3\sqrt{2}+2\sqrt{3}}=\sqrt{\left(3\sqrt{2}\right)^2-\left(2\sqrt{3}\right)^2}=\sqrt{18-12}=\sqrt{6}\)
\(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{19+2\sqrt{18}}=\left|3-2\sqrt{2}\right|+\sqrt{\left(3\sqrt{2}+1\right)^2}=3-2\sqrt{2}+3\sqrt{2}+1=4+\sqrt{2}\)
\(\dfrac{\sqrt{8-\sqrt{15}}}{\sqrt{30}-\sqrt{2}}=\dfrac{\sqrt{16-2\sqrt{15}}}{2\left(\sqrt{15}-1\right)}=\dfrac{\sqrt{\left(\sqrt{15}-1\right)^2}}{2\left(\sqrt{15}-1\right)}=\dfrac{\sqrt{15}-1}{2\left(\sqrt{15}-1\right)}=\dfrac{1}{2}\)
