\(a,\left(\sqrt{2}+2\right)\sqrt{2}-2\sqrt{2}\\ =2+2\sqrt{2}-2\sqrt{2}\\ =2\\ b,\sqrt{12}+5\sqrt{3}-\sqrt{48}\\ =\sqrt{4\cdot3}+5\sqrt{3}-\sqrt{16\cdot3}\\ =2\sqrt{3}+5\sqrt{3}-4\sqrt{3}\\ =3\sqrt{3}\\ c,\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{2}+3\right)^2}\\ =\left|1-\sqrt{2}\right|+\left|\sqrt{2}+3\right|\\ =\sqrt{2}-1+3+\sqrt{2}\\ =2\sqrt{2}+2\)
\(d,\sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}}\\ =\sqrt{2+2\sqrt{6}+3}+\sqrt{5-2\sqrt{15}+3}\\ =\sqrt{\left(\sqrt{2}\right)^2+2\cdot\sqrt{2}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}\\ =\sqrt{\left(\sqrt{2}+\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\\ =\sqrt{3}+\sqrt{2}+\sqrt{5}-\sqrt{3}\\ =\sqrt{2}+\sqrt{5}\)
a: \(\left(2+\sqrt{2}\right)\cdot\sqrt{2}-2\sqrt{2}\)
\(=2\sqrt{2}+2-2\sqrt{2}\)
=2
b: \(\sqrt{12}+5\sqrt{3}-\sqrt{48}\)
\(=2\sqrt{3}+5\sqrt{3}-4\sqrt{3}\)
\(=3\sqrt{3}\)
c: \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{2}+3\right)^2}\)
\(=\left|1-\sqrt{2}\right|+\left|3+\sqrt{2}\right|\)
\(=\sqrt{2}-1+3+\sqrt{2}=2+2\sqrt{2}\)
d: \(\sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}}\)
\(=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
\(=\sqrt{3}+\sqrt{2}+\sqrt{5}-\sqrt{3}=\sqrt{2}+\sqrt{5}\)
