a)
-5(0,4\sqrt7-1,2\sqrt5)=-5*0,4\sqrt7+5*1,2\sqrt5=-2\sqrt7+6\sqrt5=6\sqrt5-2\sqrt7
b)
\sqrt3(2\sqrt3-30)=2*\sqrt3*\sqrt3-30\sqrt3=2*3-30\sqrt3=6-30\sqrt3
c)
\frac{1}{2}\sqrt6(10\sqrt6+4\sqrt{\frac{1}{6}})==\frac{10}{2}*\sqrt6*\sqrt6+\frac{4}{2}*\sqrt6*\frac{1}{\sqrt6}=5*6+2*1=30+2=32
d)
3\sqrt2(5-\frac{1}{6}\sqrt8+\frac{\sqrt2}{2})=3\sqrt2(5-\frac{1}{6}*2\sqrt2+\frac{\sqrt2}{2})=3\sqrt2(5-\frac{1}{3}\sqrt2+\frac{\sqrt2}{2})=
15\sqrt2-\frac{3}{3}*\sqrt2*\sqrt2+\frac{3\sqrt2*\sqrt2}{2}=15\sqrt2-2+\frac{3*2}{2}=15\sqrt2-2+3=15\sqrt2+1
e)
\frac{2}{3}\sqrt3(5\sqrt3-4\sqrt{27}-12)=\frac{2}{3}\sqrt3(5\sqrt3-4*3\sqrt3-12)=\frac{2}{3}\sqrt3(5\sqrt3-12\sqrt3-12)=\frac{2}{3}\sqrt3(-7\sqrt3-12)=
-\frac{14}{3}*3-\frac{24}{3}\sqrt3=-14-8\sqrt3
f)
-0,1\sqrt{15}(\sqrt{15}-2\sqrt5+20)=-0,1*15+0,2\sqrt{75}-2\sqrt{15}=-1,5+\sqrt{0,04*75}-2\sqrt{15}=-1,5+\sqrt3-2\sqrt{15}
http://www.wolframalpha.com/input/?i=-0.1\sqrt{15}%28\sqrt{15}-2\sqrt5%2B20%29%3D-1.5%2B\sqrt3-2\sqrt{15}
g)
(5-2\sqrt7)(5+2\sqrt7)=25+10\sqrt7-10\sqrt7-4*7=25-28=-3
h)
(3-2\sqrt2)(5+\sqrt2)=15+3\sqrt2-10\sqrt2-2*2=11-7\sqrt2