a)[tex] \sqrt{144} +( \sqrt{12} +2 \sqrt{72} -6 \sqrt{18} )=12+(2 \sqrt{3} +12\sqrt{2} -18 \sqrt{2} )=[/tex][tex]12+ 2\sqrt{3} -6\sqrt{2}[/tex]
b)[tex] \sqrt{242} *( \sqrt{28} -\sqrt{7} -2 \sqrt{7} )=11\sqrt{2}*(2 \sqrt{7} -\sqrt{7} - 2\sqrt{7} )=11\sqrt{2}*(-\sqrt{7})=11\sqrt{14}[/tex]
c)[tex] \sqrt{2 \frac{1}{4} } + \sqrt{0,(4)} + \sqrt{ \frac{256}{36} } =\sqrt{ \frac{9}{4} }+\sqrt{ \frac{4}{9} }+ \frac{16}{6} = \frac{3}{2} + \frac{2}{3} + \frac{16}{6} = \frac{3*3+2*2+16}{6} [/tex][tex]= \frac{29}{6} [/tex]
d)[tex] (\sqrt{0,01} - \sqrt{0,0016} )*100=(\sqrt{ \frac{1}{100} } - \sqrt{ \frac{16}{10000} } )*100=(\frac{1}{10}-\frac{4}{100})*100[/tex][tex]= \frac{10-4}{100}*100= \frac{6}{100}*100=6 [/tex]
e) [tex] \sqrt{12} ( \sqrt{108} -2 \sqrt{48} )- \sqrt{18} ( \sqrt{288} - \sqrt{7} )=[/tex][tex]2 \sqrt{3} (6 \sqrt{3}-4 \sqrt{3})-3 \sqrt{2}(12 \sqrt{2} - \sqrt{7} )=2 \sqrt{3} *2 \sqrt{3} -36 \sqrt{4} +3 \sqrt{14} =[/tex][tex]4\sqrt{9} -36*2+3 \sqrt{14} =4*3-72+3 \sqrt{14}=-60+3 \sqrt{14} [/tex]
f)[tex]\sqrt{18} ( 3\sqrt{50} + \sqrt{162} )- \sqrt{12} ( \sqrt{432} - \sqrt{192} )=[/tex][tex]3\sqrt{2} ( 15\sqrt{2} + 9\sqrt{2} )- 2\sqrt{3} (12 \sqrt{3} -8 \sqrt{3} )=3\sqrt{2} *24\sqrt{2} -2\sqrt{3} *4\sqrt{3} =[/tex][tex]72\sqrt{4} -8\sqrt{9}=72*2-8*3=144-24=120[/tex]
