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[latex]10)=2 sqrt{2} - 3sqrt{4*2} + sqrt{16*2} =2 sqrt{2}-3*2sqrt{2} +4 sqrt{2} =6 sqrt{2} -6 sqrt{2} \=0\ \11)= sqrt{3} * sqrt{3} - sqrt{12} * sqrt{3} + sqrt{27} * sqrt{3} -3 sqrt{3} =3- sqrt{36} + sqrt{81} -3 sqrt{3} \=3-6+9-3 sqrt{3} =6-3 sqrt{3} [/latex] [latex]12)=(7^{-0,7-0,4+(-0,9)})^{ frac{1}{2}}=(7^{-2})^{ frac{1}{2} }=7^{-2* frac{1}{2} }=7^{-1}= frac{1}{7} \ \ 13)=(2*8)^{ frac{1}{2} }+(12*3)^{ frac{1}{2} }= sqrt{16} + sqrt{36}=4+6=10 [/latex] [latex]14)=3^{ frac{1}{3} }*(3^{3})^{ frac{2}{3} }*3^{-2}=3^{ frac{1}{3}+3* frac{2}{3} +(-2)}=3^{ frac{1}{3} }= sqrt[3]{3} \ \ 15)=( sqrt[3]{8}^{2} -sqrt{9} - sqrt[4]{ frac{1}{16} } )^{-2}=(4-2- frac{1}{2} )^{-2}=(1 frac{1}{2} )^{-2}=( frac{3}{2})^{-2}= frac{4}{9} [/latex] [latex]16)=( frac{1}{5} - frac{9}{4} )^{-1}=( frac{4}{20} - frac{45}{20} )^{-1}=(- frac{41}{20} )^{-1}=- frac{20}{41} \ \ 17)=(2^{7-(-6)})^{3}*2^{-4}=2^{13*3-4}=2^{35} \ [/latex] [latex]18)=(-3)^{5+4-6}=-3)^{3}=-27 \ \ 19)= frac{( frac{1}{3} *6)^{3}}{ (frac{1}{4} *4)^{3}}}=2^{3}=8 \ \ 20)=frac{5*5^{14}}{5^{15}}=frac{5^{15}}{5^{15}}=1[/latex] [latex]21)x+y=2- sqrt{5} +2+ sqrt{5} =4 \ \ x-y=2- sqrt{5} -2- sqrt{5} =-2 sqrt{5} \ \2y-3x=4+2 sqrt{5} -6+3 sqrt{5} =5 sqrt{5} -2 \ \ frac{y}{x}=frac{2+ sqrt{5}}{2- sqrt{5} }*frac{2+ sqrt{5} }{2+ sqrt{5}} = frac{4+4 sqrt{5}+5 }{4-5} =-9-4 sqrt{5} \ \xy=(2-sqrt{5})(2+sqrt{5})=2^{2}-sqrt{5}^{2}=4-5=-1\ \ x^{2} =(2-sqrt{5})^{2}=2^{2}-2*2*sqrt{5}+sqrt{5}^{2}=4-4sqrt{5}+5=9-4sqrt{5}\ \-frac{1}{2}y^{2}=-frac{1}{2}(2+sqrt{5})^{2}=-frac{1}{2}(4+4sqrt{5}+5)=[/latex] [latex]=- frac{9}{2} -2 sqrt{5} [/latex]