\(a,\left(\sqrt{2}+2\right).\sqrt{2}-2\sqrt{2}\)
\(=2+2\sqrt{2}-2\sqrt{2}\)
\(=2\)
\(b,\sqrt{\left(\sqrt{5}-\sqrt{10}\right)^2}-\sqrt{10.\left(\sqrt{2+1}\right)^2}\)
\(=\left|\sqrt{5}-\sqrt{10}\right|-\sqrt{10.3}\)
\(=\left(\sqrt{10}-\sqrt{5}\right)-\sqrt{30}\)
\(=\sqrt{10}-\sqrt{5}-\sqrt{30}\)
\(=\sqrt{5}.\left(\sqrt{2}-1-\sqrt{6}\right)\)
\(c,\left(\sqrt{2}+\sqrt{3}\right)^2.\sqrt{49-20\sqrt{6}}\)
\(=\left(2+3+2.\sqrt{2}.\sqrt{3}\right).\sqrt{\left(5-2\sqrt{6}\right)^2}\)
\(=\left(5+2\sqrt{6}\right).\left(5-2\sqrt{6}\right)\)
\(=1\)
d,\(\dfrac{2}{\sqrt{8-\sqrt{60}}}-\sqrt{\dfrac{\sqrt{18}+\sqrt{27}}{\sqrt{3}+\sqrt{2}}}\)
\(=\dfrac{2}{\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}-\sqrt{\dfrac{3\sqrt{2}+3\sqrt{3}}{\sqrt{3}+\sqrt{2}}}\)
\(=\dfrac{2}{\sqrt{5}-\sqrt{3}}-\sqrt{\dfrac{3.\left(\sqrt{2}+\sqrt{3}\right)}{\sqrt{3}+\sqrt{2}}}\)
\(=\dfrac{2}{\sqrt{5}-\sqrt{3}}-\sqrt{3}\)
\(=\dfrac{2.\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}-\sqrt{3}\)
\(=\dfrac{2\sqrt{5}+2\sqrt{3}}{2}-\sqrt{3}\)
\(=\dfrac{2\sqrt{5}+2\sqrt{3}-2\sqrt{3}}{2}\)
\(=\dfrac{2\sqrt{5}}{2}\)
\(=\sqrt{5}\)
