Oblicz : a)[latex] sqrt[3]{1000} + sqrt{16} [/latex] b)[latex] sqrt[3]{ 5^{2}+ 10^{2} } [/latex] c)[latex] sqrt{ 5^{2} } + sqrt[3]{ 17^{3} } [/latex] d)[latex] frac{ sqrt{72}+ sqrt{2} }{ sqrt{2} } [/latex] e)[latex] sqrt[3]{2} x sqrt[3]{32} + sqrt2}

[latex]a) sqrt[3]{1000} + sqrt{16} = sqrt[3]{10^3}+sqrt{4^2}=10+4 = 14\ b) sqrt[3]{ 5^{2}+ 10^{2} } =sqrt[3]{25+100}=sqrt[3]{125}=sqrt[3]{5^3}=5\ c) sqrt{ 5^{2} } + sqrt[3]{ 17^{3} } = 5+17 = 22\ d) frac{ sqrt{72}+ sqrt{2} }{ sqrt{2} } = frac{6sqrt{2}+sqrt{2}}{sqrt{2}}=frac{7sqrt{2}}{sqrt{2}}=7\ e) sqrt[3]{2} cdot sqrt[3]{32} + sqrt2} cdot sqrt{8} =sqrt[3]{2cdot 32} + sqrt{2cdot 8}=sqrt[3]{64}+sqrt{16}=\=sqrt[3]{4^3}+sqrt{4^2}=4+4=8 [/latex]

[latex] a) quad sqrt[3]{1000} + sqrt{16} = sqrt[3]{10^3}+sqrt{4^2}=10+4 = oxed{14} \ \ \ b) quad sqrt[3]{ 5^{2}+ 10^{2} } =sqrt[3]{25+100}=sqrt[3]{125}=sqrt[3]{5^3}= oxed{5} [/latex] [latex]c) quad sqrt{ 5^{2} } + sqrt[3]{ 17^{3} } = 5+17 = oxed{22} \ \ \ d) quaddfrac{ sqrt{72}+ sqrt{2} }{ sqrt{2} } = dfrac{ sqrt{2^3*3^2}+ sqrt{2} }{ sqrt{2} } =dfrac{ sqrt{2^2*2*3^2}+ sqrt{2} }{ sqrt{2} } = \ \ \ dfrac{ 2*3sqrt{2}+ sqrt{2} }{ sqrt{2} } = dfrac{ 6sqrt{2}+ sqrt{2} }{ sqrt{2} } =dfrac{ sqrt{2}(6+1) }{ sqrt{2} } = dfrac{ ot sqrt ot{2}(6+1) }{ otsqrt ot{2} } = \ \ 6+1= oxed{7}[/latex] [latex]e) sqrt[3]{2}* sqrt[3]{32} + sqrt2} * sqrt{8} = sqrt[3]{2}* sqrt[3]{2^5} + sqrt2} * sqrt{2^3} = \ \ \ sqrt[3]{2*2^5} + sqrt{2*2^3} = sqrt[3]{2^6} + sqrt{2^4} = 2^{ frac{6}{3}} +2^{ frac{4}{2}}= 2^2+2^2= 4+4= oxed{8} [/latex]