Proszę o pomoc. 1. Oblicz: √2 i 7/9= √6+19= ∛54/∛2= ∛27= ∛16×∛4= ∛3 i 3/8= √7×49×36= ∛25÷∛1/5= √ czwartego stopnia z 2√64= √25×16= ∛4×∛2= √8÷√2= ∛4/3÷∛9/2= ∛2 do potęgi 5×2 do potęgi 4×2³= Z góry DZIĘKUJĘ .

[latex]sqrt{2frac{7}{9}} = sqrt{frac{25}{9}} = frac{5}{3}=1frac{2}{3}\\sqrt{6+19} = sqrt{25} = 5\\frac{sqrt[3]{54}}{sqrt[3]{2}} = sqrt[3]{frac{54}{2}} = sqrt[3]{27} = 3\\sqrt[3]{27} = 3\\sqrt[3]{16}cdotsqrt[3]{4} = sqrt[3]{16cdot4} = sqrt[3]{64} = 4\\sqrt{3frac{3}{8}}=sqrt[3]{frac{27}{8}} = frac{3}{2} = 1frac{1}{2}\\sqrt{7cdot49cdot36} = sqrt{12348} = sqrt{36cdot343} = 6sqrt{343}[/latex] [latex]sqrt[3]{25}:sqrt[3]{frac{1}{5}}=sqrt[3]{25:frac{1}{5}} = sqrt[3]{25cdot5} = sqrt[3]{125} = 5\\sqrt[4]{2sqrt{64}}=sqrt[4]{2cdot8} = sqrt[4]{16} = 2\\sqrt{25cdot16} = sqrt{25}cdotsqrt{16} = 5cdot4 = 20\\sqrt[3]{4}cdotsqrt[3]{2} = sqrt[3]{4cdot2} = sqrt[3]{8} = 2\\sqrt{8}:sqrt{2} = sqrt{8:2} = sqrt{4} = 2\\sqrt[3]{frac{4}{3}}:sqrt[3]{frac{9}{2}}=sqrt[3]{frac{4}{3}:frac{9}{2}}=sqrt[3]{frac{4}{3}cdotfrac{2}{9}} = sqrt[3]{frac{8}{27}}=frac{2}{3}[/latex] [latex]sqrt[3]{2^{5}cdot2^{4}cdot2^{3}}}=sqrt[3]{2^{5+4+3}}}=sqrt[3]{2^{12}}=(2^{12})^{frac{1}{3}} = 2^{4} = 16[/latex]

1) [latex] sqrt{2 frac{7}{9} } = sqrt{ frac{25}{9} } = frac{5}{3} = 1 frac{2}{3} [/latex] [latex] sqrt{6 + 19} = sqrt{25} =5[/latex] [latex] frac{ sqrt[3]{54} }{ sqrt[3]{2} } = frac{ sqrt[3]{2*27} }{ sqrt[3]{2} } = frac{3 sqrt[3]{2} }{ sqrt[3]{2} } = 3[/latex] [latex] sqrt[3]{27} =3[/latex] [latex] sqrt[3]{16} * sqrt[3]{4} = sqrt[3]{16*4} = sqrt[3]{64} = 4[/latex] [latex] sqrt[3]{3 frac{3}{8} } = sqrt[3]{ frac{27}{8} } = frac{3}{2} = 1 frac{1}{2} [/latex] [latex] sqrt{7*49*36} =7*6 sqrt{7} = 42 sqrt{7} [/latex] [latex] sqrt[3]{25} : sqrt[3]{ frac{1}{5} } = sqrt[3]{25: frac{1}{5} } = sqrt[3]{25*5} = sqrt[3]{125} = 5[/latex] [latex] sqrt[4]{2* sqrt{64} } = sqrt[4]{2 * 8} = sqrt[4]{16} = 2[/latex] [latex] sqrt{25*16} = 5 * 4 = 20[/latex] [latex] sqrt[3]{4} * sqrt[3]{2} = sqrt[3]{4*2} = sqrt[3]{8} = 2[/latex] [latex] sqrt{8} : sqrt{2} = sqrt{8:2} = sqrt{4} =2[/latex] [latex] sqrt[3]{ frac{4}{3} } : sqrt[3]{ frac{9}{2} } = sqrt[3]{ frac{4}{3} : frac{9}{2} } = sqrt[3]{ frac{4*2}{3*9} } = sqrt[3]{ frac{8}{27} } = frac{2}{3} [/latex] [latex] sqrt[3]{ 2^{5}* 2^{4} * 2^{3} } = sqrt[3]{32*16*8} = sqrt[3]{4096} = 16[/latex]