Zapisz w prostszej postaci :   a) [latex]sqrt{2+sqrt{2}} * sqrt{2(2-sqrt{2})}[/latex]   b)[latex]frac{1}{sqrt{5-1}} + frac{1-sqrt{5}}{4}[/latex]

a) [latex]sqrt{2+sqrt{2}} cdot sqrt{2 cdot (2-sqrt{2})} = sqrt{(2+sqrt{2}) cdot 2 cdot (2-sqrt{2})} =\ = sqrt{2 cdot (2+sqrt{2})(2-sqrt{2})} = sqrt{2 cdot (2^2-(sqrt{2})^2)} = sqrt{2 cdot (4-2)} =\ = sqrt{2 cdot 2} = sqrt{4} =2[/latex]   b) [latex]frac{1}{sqrt{5-1}} + frac{1-sqrt{5}}{4} = frac{1}{sqrt{4}} + frac{1-sqrt{5}}{4} = frac{1}{2} + frac{1-sqrt{5}}{4} = frac{2}{4} + frac{1-sqrt{5}}{4} = frac{2+1-sqrt{5}}{4} = \\ = frac{3-sqrt{5}}{4}[/latex]     --------------------------- Jeśli w b) jest błąd w zapisie i - 1 nie jest pod pierwiastkiem, to wtedy: [latex]frac{1}{sqrt{5}-1} + frac{1-sqrt{5}}{4} =frac{sqrt{5}+1}{(sqrt{5}-1)(sqrt{5}+1)} + frac{1-sqrt{5}}{4} =frac{sqrt{5}+1}{(sqrt{5})^2-1^2} + frac{1-sqrt{5}}{4} = \\ =frac{sqrt{5}+1}{5 - 1} + frac{1-sqrt{5}}{4} =frac{sqrt{5}+1}{4} + frac{1-sqrt{5}}{4} =frac{sqrt{5}+1+1-sqrt{5}}{4} = frac{2}{4} = frac{1}{2}[/latex]  

1. Zapisz w prostszej postaci: [latex] frac{10 sqrt[3]{-12} }{2} -4( sqrt[3]{12} - 5) [/latex] [latex] sqrt{ 3^{3} } - frac{1}{5} sqrt{75} + 2 sqrt{48} [/latex] 2. Usuń niewymierność z mianownika ułamka [latex] frac{3 sqrt{2} +5 }{2 sqrt{3} } [/latex]

1. Zapisz w prostszej postaci: [latex] frac{10 sqrt[3]{-12} }{2} -4( sqrt[3]{12} - 5) [/latex] [latex] sqrt{ 3^{3} } - frac{1}{5} sqrt{75} + 2 sqrt{48} [/latex] 2. Usuń niewymierność z mianownika ułamka [latex] frac{3 sqrt{2} +5 }{2 sqrt{3} }...

Zapisz w prostszej postaci. a)[latex]frac{3sqrt{5}-sqrt{20}}{sqrt{12}}[/latex] b)[latex](sqrt{10}-2sqrt{5})*sqrt{10}[/latex]   c)[latex](4sqrt{3}+3sqrt{2})*sqrt{6}[/latex] d)[latex]frac{sqrt{40}-sqrt{160}}{sqrt{90}}[/latex] Potrzebuje jak najszybciej !!!

Zapisz w prostszej postaci. a)[latex]frac{3sqrt{5}-sqrt{20}}{sqrt{12}}[/latex] b)[latex](sqrt{10}-2sqrt{5})*sqrt{10}[/latex]   c)[latex](4sqrt{3}+3sqrt{2})*sqrt{6}[/latex] d)[latex]frac{sqrt{40}-sqrt{160}}{sqrt{90}}[/latex] Potrzebuje jak najszybci...

Zapisz wyrażenia w prostszej postaci:   a) [latex]sqrt{32} +5sqrt{2} - sqrt{200} + sqrt{2}[/latex]   b) [latex]frac{sqrt{2} + 3sqrt{8}- sqrt{18}}{sqrt{2}}[/latex]   c) [latex]sqrt{24} * sqrt{3}[/latex]   d) [latex]4sqrt{3} + sqrt{27}[/latex]

Zapisz wyrażenia w prostszej postaci:   a) [latex]sqrt{32} +5sqrt{2} - sqrt{200} + sqrt{2}[/latex]   b) [latex]frac{sqrt{2} + 3sqrt{8}- sqrt{18}}{sqrt{2}}[/latex]   c) [latex]sqrt{24} * sqrt{3}[/latex]   d) [latex]4sqrt{3} + sqrt{27}[/latex]...

Zapisz w prostszej postaci : [latex] a).- frac{10 sqrt[3]{-12} }{2} - 4 ( sqrt[3]{12} -5) b). sqrt{3 ^{3} } - frac{1}{5} sqrt{75} + 2 sqrt{48} [/latex]

Zapisz w prostszej postaci : [latex] a).- frac{10 sqrt[3]{-12} }{2} - 4 ( sqrt[3]{12} -5) b). sqrt{3 ^{3} } - frac{1}{5} sqrt{75} + 2 sqrt{48} [/latex]...

Zapisz w prostszej postaci: [latex]frac{5a*2a^{2}}{20} \ frac{6x^{2}y}{3y} \ frac{15m^{3}n^{2}}{10n} \ frac{3bc}{bc^{3}} \ frac{s^{3}t^{2}sqrt{2}}{st} \ frac{2n^{2}*6v^{3}}{4n^{2}v} \ frac{2p^{3}*9q^{4}}{90p^{2}q^{2}}[/latex]

Zapisz w prostszej postaci: [latex]frac{5a*2a^{2}}{20} \ frac{6x^{2}y}{3y} \ frac{15m^{3}n^{2}}{10n} \ frac{3bc}{bc^{3}} \ frac{s^{3}t^{2}sqrt{2}}{st} \ frac{2n^{2}*6v^{3}}{4n^{2}v} \ frac{2p^{3}*9q^{4}}{90p^{2}q^{2}}[/latex]...

Zad.1 Zapisz w prostszej postaci: [latex]-5( sqrt[3]{13} - 4) - frac{6 sqrt[3]{-13} }{2} [/latex]

Zad.1 Zapisz w prostszej postaci: [latex]-5( sqrt[3]{13} - 4) - frac{6 sqrt[3]{-13} }{2} [/latex]...