Rút gọn:
a)(\(\sqrt{8}-3\sqrt{2}+\sqrt{10}\))\(.\sqrt{2}-\sqrt{5}\)
b)(\(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{2}\)+\(\frac{4}{5}\sqrt{200}\))\(:\frac{1}{8}\)
c)(\(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\))\(.\frac{1}{\sqrt{6}}\)
d)(\(\frac{\sqrt{14}-\sqrt{2}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\))\(:\frac{1}{\sqrt{7}-\sqrt{5}}\)
a) Ta có: \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}\)
\(=\left(-\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}\)
\(=-2+2\sqrt{5}-\sqrt{5}\)
\(=-2+\sqrt{5}\)
b) \(\left(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\sqrt{200}\right)\div\frac{1}{8}\)
\(=\left(\frac{\sqrt{2}}{4}-\frac{3\sqrt{2}}{2}+8\sqrt{2}\right)\cdot8\)
\(=\frac{27\sqrt{2}}{4}\cdot8\)
\(=54\sqrt{2}\)
c) \(\left(\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\frac{\sqrt{216}}{3}\right)\cdot\frac{1}{\sqrt{6}}\)
\(=\left[\frac{\left(2\sqrt{3}-\sqrt{6}\right)\left(\sqrt{8}+2\right)}{8-4}-\frac{6\sqrt{6}}{3}\right]\cdot\sqrt{6}\)
\(=\left(\frac{4\sqrt{6}+4\sqrt{3}-4\sqrt{3}-2\sqrt{6}}{4}-2\sqrt{6}\right)\cdot\sqrt{6}\)
\(=\left(\frac{\sqrt{6}}{2}-2\sqrt{6}\right)\cdot\sqrt{6}\)
\(=3-12=-9\)
