a) √[2 14/25]= =√[64/25]= =√[8/5]²= =8/5= =1 3/5 ----------------------- b) ∛[2 10/27]= =∛[64/27]= =∛[4/3]³= =4/3= =1 1/3 ----------------------- c) √2 * √8= =√[2*8]= =√16= =4 lub [zapis jest niejasny] √[2*√8]= =√[2*2√2]= =√[4√2]= =2√(√2)= =2⁴√2 ----------------------- d) ∛[4/75] * ∛[1 1/5]= =∛[4/75] * ∛[6/5]= =∛[4/75 * 6/5]= =∛[24/375]= =∛[8/125]= =∛[2/5]³= =2/5
[latex]a) sqrt{2 frac{14}{25}}}= sqrt{frac{64}{25}}=frac{sqrt{64}}{sqrt{25}} = frac{8}{5} =1frac {3}{5} [/latex] [latex]b) sqrt[3]{2 frac{10}{27}}= sqrt[3] {frac{64}{27}}= frac{sqrt[3]{64}}{sqrt[3]{27}} = frac{4}{3} = 1frac{1}{3} [/latex] [latex]c) sqrt[3]{frac{4}{75}} * sqrt[3]{1frac{1}{5}}=sqrt[3]{frac{4}{75} * 1frac{1}{5}}= sqrt[3]{frac{4}{75} * frac{6}{5}}= sqrt[3]{frac{24}{375}} = sqrt[3]{frac{8}{125}} =\ = frac{sqrt[3]{8}}{sqrt[3]{125}} = frac{2}{5} [/latex] [latex]d) sqrt[3]{frac{4}{75}} * sqrt[3]{1frac{1}{5}} = sqrt[3] {frac{4}{75} * 1frac{1}{5}} = sqrt[3] {frac{4}{75} * frac{6}{5}} = sqrt[3]{frac{24}{375}} = \ frac{sqrt[3]{24}}{sqrt[3]{375}} = frac{sqrt[3]{8*3}}{sqrt[3]{125*3}} == frac{2sqrt[3]{3}}{3sqrt[3]{3}} = frac {2}{3}[/latex]
