Oblicz [latex] sqrt{279} [/latex] [latex] sqrt{279} (3sqrt{2} + sqrt{18} -2 sqrt{8}) - sqrt{2} ( sqrt{54} : sqrt{3} ) : sqrt{2} sqrt{1 + frac{1}{9} } [/latex]

[latex]sqrt{279}=sqrt{9 cdot 31}=3 sqrt{31} [/latex] ===================== [latex](3sqrt{2} + sqrt{18} -2 sqrt{8}) cdot sqrt{2}=[/latex] [latex]3sqrt{2}cdot sqrt{2} + sqrt{18}cdot sqrt{2} -2 sqrt{8} cdot sqrt{2}=[/latex] [latex]3sqrt{2cdot 2} + sqrt{18cdot 2} -2 sqrt{8 cdot 2}=[/latex] [latex]3sqrt{4} + sqrt{36} -2 sqrt{16}=[/latex] [latex]6 +6 -8=4[/latex] ===================== [latex]( sqrt{54} : sqrt{3} ) : sqrt{2}=[/latex] [latex]sqrt{54:3} : sqrt{2}=[/latex] [latex]sqrt{18} : sqrt{2}=[/latex] [latex]sqrt{18 :2}=[/latex] [latex]sqrt{9}=3[/latex] ===================== [latex] sqrt{1 + frac{1}{9} } = sqrt{ frac{10}{9} }= frac{ sqrt{10} }{3} [/latex]