masz jak na razie zadanie 7, bo jestem dopiero w trakcie robienia 8 :)
[latex]7.\ a) (4-2sqrt{5})cdot(sqrt{5}+3)=4sqrt{5}+12-2cdot5-6sqrt{5}=\ =-2sqrt{5}+2[/latex] [latex]b) (2sqrt{6}+6)cdot(2sqrt{3}-3sqrt{2})=4sqrt{18}-6sqrt{12}+12sqrt{3}-18sqrt{2}=\ =4cdot3sqrt{2}-6cdot2sqrt{3}+12sqrt{3}-18sqrt{2}=-6sqrt{2}[/latex] [latex]c) (9-2sqrt{15})cdot(3sqrt{3}+2sqrt{5})=\ 27sqrt{3}+18sqrt{5}-6cdot3sqrt{5}-4cdot5sqrt{3}=\ 7sqrt{3}[/latex] [latex]d) (2sqrt{5}-sqrt{2})cdot(sqrt{10}+3)=\ =2cdot5sqrt{2}+6sqrt{5}-2sqrt{5}-3sqrt{2}=\ =4sqrt{5}+7sqrt{2}[/latex] [latex]8.\ a) sqrt[3]{4}cdotsqrt[3]{250}-sqrt{7}cdotsqrt{63}=sqrt[3]{1000}-sqrt{441}=10-21=-11[/latex] [latex]b) sqrt{15}cdotsqrt{frac{3}{5}}+sqrt[3]{20}cdotsqrt[3]{frac{2}{5}}=sqrt{9}+sqrt[3]{8}=3+2=5[/latex] [latex]c) (sqrt[3]{24}-2sqrt[3]{81}+sqrt[3]{192}):sqrt[3]{3}=\ =(2sqrt[3]{3}-2cdot3sqrt[3]{3}+4sqrt[3]{3}):sqrt[3]{3}=0[/latex] [latex]d) sqrt[3]{1frac{9}{16}}cdotsqrt[3]{(sqrt{frac{5}{4})}^{2}}=\ =sqrt[3]{frac{25}{16}}cdotsqrt[3]{frac{5}{4}}=sqrt[3]{frac{125}{64}}=frac{5}{4}[/latex] [latex]e) sqrt[3]{3frac{3}{4}}cdotsqrt[3]{4frac{1}{6}}-sqrt{2frac{7}{9}}=\ =sqrt[3]{frac{15cdot25}{4cdot6}}-sqrt{frac{25}{9}}=\ =frac{5}{2}-frac{5}{3}=frac{15-10}{6}=frac{5}{6}[/latex] [latex]sqrt{sqrt[3]{216}+sqrt[3]{32}+1}=sqrt{6+1+2sqrt[3]{4}}[/latex]
