a)
\frac{4^{\frac{1}{2}}*4^{-1}}{4^0-0,5}=\frac{4^{-\frac{1}{2}}}{1-\frac{1}{2}}=\frac{(2^2)^{-\frac{1}{2}}}{\frac{1}{2}}=\frac{2^{-1}}{2^{-1}}=1
b)
\sqrt{6+\sqrt{7+\sqrt4}}=\sqrt{6+\sqrt{7+2}}=\sqrt{6+\sqrt9}=\sqrt{6+3}=\sqrt9=3
c)
(2\sqrt[3]{1\frac{4}{5}} + \sqrt[3]{-8\frac{1}{3}}) * \sqrt[3]{-0,12} =
= 2\sqrt[3]{\frac{9}{5}*(-\frac{12}{100})} + \sqrt[3]{(-\frac{25}{3})*(-\frac{12}{100})} =
= -2\sqrt[3]{\frac{108}{500}} + \sqrt[3]{\frac{300}{300}} = -2\sqrt[3]{0,216}+1=
=-2*0,6+1=-1,2+1=-0,2
d)
(3\sqrt2-3)^2*(3\sqrt2+3)^2=(9*2-18\sqrt2+9)(9*2+18\sqrt2+9)=(27-18\sqrt2)(27+18\sqrt2)=
=27^2-(18\sqrt2)^2=729-324*2=729-948=81
e)
(9+\sqrt{11})^2-(9-\sqrt{11})^2=81+18\sqrt{11}+11-(81-18\sqrt{11}+11)=92+18\sqrt{11}-(92-18\sqrt{11}=
=92+18\sqrt{11}-92+18\sqrt{11}=36\sqrt{11}
f)
(\sqrt{8-\sqrt{15}}+\sqrt{8+\sqrt{15}})^2=
=8-\sqrt{15}+2*\sqrt{(8-\sqrt{15})(8+\sqrt{15})}+8+\sqrt{15}=
=16+2\sqrt{64-15}+8=16+2\sqrt{49}=16+2*7=30