1) [latex]3 sqrt{2} + frac{5}{7 sqrt{2} }=3 sqrt{2} + frac{5sqrt{2}}{7 sqrt{2}cdot sqrt{2}}=[/latex] [latex]3 sqrt{2} + frac{5sqrt{2}}{14}= frac{52 sqrt{2} }{14}+ frac{5sqrt{2}}{14}=[/latex] [latex]frac{42 sqrt{2}+5sqrt{2}}{14}=frac{47sqrt{2}}{14}[/latex] 2) [latex]frac{ sqrt[3]{-81}cdot sqrt[3]{375} }{ sqrt[3]{-3} }=frac{ sqrt[3]{-3^4}cdot sqrt[3]{125cdot 3} }{ sqrt[3]{-3} }=[/latex] [latex]frac{ sqrt[3]{-3^4cdot 125cdot 3} }{ sqrt[3]{-3} }=frac{ sqrt[3]{-3^3cdot 5^3cdot 3^2} }{ sqrt[3]{-3} }=[/latex] [latex]frac{5cdot 3 sqrt[3]{-3^2} }{ sqrt[3]{-3} }=15cdot sqrt[3]{frac{-3^2}{-3}} =15 sqrt[3]{3}[/latex]
Oblicz: [latex] sqrt[3]{192} [/latex] [latex] sqrt[3]{375} [/latex] [latex] sqrt{20 frac{1}{4} } [/latex] [latex] sqrt[3]{3 frac{3}{8} } [/latex] [latex] sqrt{-16} [/latex] [latex] sqrt[3]{-125} [/latex]...
Oblicz: a) [latex]frac{(2)^{-2}+5^{0}}{(0,5)^{-2}-5cdot(-2)^{2}+(frac{2}{3})^{-2}}+4,75=[/latex] b) [latex]frac{[(frac{1}{2})^{-1}-0,25^{-1}]^{-2}}{0,375^{-1}-0,6^{-1}}=[/latex] c) [latex](sqrt{sqrt{2}-1}+(sqrt{sqrt{2}+1})^{2}[/latex]...
Oblicz : [latex] sqrt[3]{0,375} * sqrt[3]{9} +( 3^{-1} - sqrt[4]{ frac{16}{81} }) ^{2} [/latex] [latex][( frac{81}{625}) ^{-0,75} :(1 frac{2}{3}) ^{3} - (0,125) ^ frac{1}{3} } ] ^{-2} [/latex]...
Oblicz: [latex]frac{4}{5}- [frac{(-2)^3}{0,2}+ frac{0,6}{0,02}: frac{6}{5}]cdot 0,2= sqrt{242} + 0,25sqrt{32} - frac{1}{3}sqrt{72}= sqrt[3]{81} + 2sqrt[3]{24} - sqrt[3]{375}= 0,5^{-5}cdot10^{6}:20^{5}= [/latex]...
oblicz sume ciągu geometrycznego [latex]sqrt{3}+3+...+27\ frac{1}{2}+frac{1}{sqrt{2}}+...+8\3sqrt{5}+15+...+375\pi+2pi+...+32pi [/latex] [/latex]...
