a: \(\sqrt{48}-\sqrt{27}+2\cdot\sqrt{147}-\sqrt{108}\)
\(=4\sqrt3-3\sqrt3+2\cdot7\sqrt3-6\sqrt3\)
\(=\sqrt3+14\sqrt3-6\sqrt3=15\sqrt3-6\sqrt3=9\sqrt3\)
b: \(-2\sqrt{12}+\frac15\cdot\sqrt{75}-\sqrt{27}\)
\(=-2\cdot2\sqrt3+\frac15\cdot5\sqrt3-3\sqrt3\)
\(=-4\sqrt3-3\sqrt3+\sqrt3=-6\sqrt3\)
c: \(2\sqrt{24}-5\sqrt{54}+\sqrt{10+4\sqrt6}\)
\(=2\cdot2\sqrt6-5\cdot3\sqrt6+\sqrt{\left(\sqrt6+2\right)^2}\)
\(=4\sqrt6-15\sqrt6+2+\sqrt6=2-10\sqrt6\)
d: \(\frac32\cdot\sqrt{24}-\frac34\cdot\sqrt{96}+\frac{2\sqrt3}{\sqrt2}-6\sqrt{\frac23}\)
\(=\frac32\cdot2\sqrt6-\frac34\cdot4\sqrt6+\sqrt6-\sqrt{36\cdot\frac23}=\sqrt6-\sqrt6+\sqrt6-\sqrt{24}\)
\(=\sqrt6-2\sqrt6=-\sqrt6\)
