1. [latex]a) sqrt{8^{2}} = sqrt{64} = 8[/latex] [latex]b) (sqrt{6})^{4} = sqrt{6^{4}} = sqrt{1296} = sqrt{36 * 36} = 36[/latex] [latex]c) sqrt{4^{6}} = sqrt{4096} = sqrt{64 * 64} = 64[/latex] [latex]d) (sqrt{10}){^{8}} = sqrt{10}{^{8}} = sqrt{100000000} = sqrt{10000*10000} = 10 000[/latex] [latex]sqrt[3]{17^{3}} = sqrt[3]{17^{3}} = sqrt[3]{17*17*17} = 17[/latex] [latex](sqrt[3]{12})^{3} = (sqrt[3]{12^{3}}) = (sqrt[3]{12*12*12}) = 12[/latex] [latex](sqrt[3]{11})^{6} = sqrt[3]{11^{2} *11^{2}*11^{2}} = 11^{2} = 121[/latex] [latex]sqrt[3]{3^{9}} = sqrt[3]{3^{3}*3^{3}*3^{3}} = 3^{3} = 27[/latex] zad. 2 Pole kwadratu: a) [latex]Pole kwadratu = a * a = sqrt{8} * sqrt{8} = sqrt{64} = 8m^2[/latex] b) [latex]Pole kwadratu = a * a =3 sqrt{2} * 3sqrt{2} =sqrt{3^{2}*2}*sqrt{3^{2}*2} = sqrt{18}*sqrt{18} = sqrt{324} = 18m^2[/latex] c) [latex]Pole kwadratu = a * a =10 sqrt{5} * 10sqrt{5} =sqrt{10^{2}*5}*sqrt{10^{2}*5} = sqrt{500}*sqrt{500} = sqrt{250000} = 500m^2[/latex] d) [latex]Pole kwadratu = a * a =2 sqrt{7} * 2sqrt{7} =sqrt{2^{2}*7}*sqrt{2^{2}*7} = sqrt{28}*sqrt{28} = sqrt{784} = 28m^2[/latex] zad 3 Objętość sześcianu = Pole podstawy * wysokość = [latex]a^{3}[/latex] a) Objętość = [latex]sqrt[3]{2}*sqrt[3]{2}*sqrt[3]{2} = sqrt[3]{2*2*2} = 2m^{3}[/latex] b) Objętość = [latex]2sqrt[3]{3} * 2sqrt[3]{3} * 2sqrt[3]{3} = sqrt[3]{2^{3}*3*2^{3}*3*2^{3}*3}=2^{3}*3 = 24dm^{3}[/latex] c) Objętość = [latex]5sqrt[3]{9} * 5sqrt[3]{9} * 5sqrt[3]{9} = sqrt[3]{5^{3}*9*5^{3}*9*5^{3}*9}=5^{3}*9 = 1125cm^{3}[/latex] d) Objętość = [latex]3sqrt[3]{12} * 3sqrt[3]{12} * 3sqrt[3]{12} = sqrt[3]{3^{3}*12*3^{3}*12*3^{3}*12}=3^{3}*12 = 324mm^{3}[/latex]
