a: \(\sqrt{12}-3\sqrt{27}-\sqrt{300}\)
\(=2\sqrt3-3\cdot3\sqrt3-10\sqrt3\)
\(=-8\sqrt3-9\sqrt3=-17\sqrt3\)
b: \(\sqrt{\left(1-\sqrt2\right)^2}-\sqrt{\left(\sqrt2+3\right)^2}\)
\(=\left|1-\sqrt2\right|-\left|\sqrt2+3\right|\)
\(=\sqrt2-1-3-\sqrt2=-4\)
c: \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\cdot\sqrt{11}+3\sqrt{22}\)
\(=\left(3\sqrt{11}-\sqrt{11}-3\sqrt2\right)\cdot\sqrt{11}+3\sqrt{22}\)
\(=22-3\sqrt{22}+3\sqrt{22}=22\)
d: \(\left(2\sqrt{112}-5\sqrt7+2\sqrt{63}-2\sqrt{28}\right)\cdot\sqrt7\)
\(=\left(2\cdot4\sqrt7-5\sqrt7+2\cdot3\sqrt7-2\cdot2\sqrt7\right)\cdot\sqrt7\)
\(=5\sqrt7\cdot\sqrt7=5\cdot7=35\)
e: \(\sqrt[3]{125}+\sqrt[3]{-27}=5-3=2\)
g: \(\left(2\sqrt{27}-3\sqrt{48}+3\sqrt{75}-\sqrt{192}\right)\left(1-\sqrt3\right)\)
\(=\left(2\cdot3\sqrt3-3\cdot4\sqrt3+3\cdot5\sqrt3-8\sqrt3\right)\left(1-\sqrt3\right)\)
\(=\sqrt3\left(1-\sqrt3\right)=\sqrt3-3\)
h: \(7\sqrt{24}-\sqrt{150}-5\sqrt{54}=7\cdot2\sqrt6-5\sqrt6-5\cdot3\sqrt6\)
\(=14\sqrt6-5\sqrt6-15\sqrt6=-6\sqrt6\)
i: \(2\sqrt{20}-\sqrt{50}+3\sqrt{80}-\sqrt{320}\)
\(=2\cdot2\sqrt5-5\sqrt2+3\cdot4\sqrt5-8\sqrt5\)
\(=4\sqrt5+12\sqrt5-8\sqrt5-5\sqrt2=8\sqrt5-5\sqrt2\)
