1. a) [latex] sqrt{ frac{49}{169}[/latex] = [latex] frac{7}{13} [/latex] b) [latex] sqrt{ frac{121}{441}[/latex] = [latex] frac{11}{21}[/latex] c) [latex] sqrt{1 frac{9}{16} } [/latex] = [latex] sqrt{ frac{25}{16}[/latex] = [latex] frac{5}{4} [/latex] d) [latex] sqrt{2 frac{14}{25} } [/latex] = [latex] sqrt{ frac{64}{25} } [/latex] = [latex] frac{8}{5} [/latex] e) [latex] sqrt{0,09} [/latex] =[latex] sqrt{ frac{9}{100}[/latex] = [latex] frac{3}{10} [/latex] f) [latex] sqrt{1,69} [/latex] = [latex] sqrt{1 frac{69}{100}[/latex] = [latex] sqrt{ frac{169}{100} [/latex] = [latex] frac{13}{10} [/latex] g) [latex] sqrt{6+ sqrt{7+} sqrt{4}[/latex] = [latex] sqrt{6+ sqrt{7+2} } [/latex] = [latex] sqrt{ 6+sqrt{9} [/latex] = [latex] sqrt{6+3} [/latex] = [latex] sqrt{9} [/latex] = [latex]3[/latex] h) [latex] sqrt{6- sqrt{6- sqrt{4}[/latex] = [latex] sqrt{6- sqrt{6-2} } [/latex] = [latex] sqrt{6- sqrt{4} [/latex] = [latex] sqrt{6-2} [/latex] = [latex] sqrt{4} [/latex] = [latex]2[/latex] 2. a) [latex]4 sqrt{1,5} [/latex] = [latex] sqrt{1,5 *16} [/latex] = [latex] sqrt{24} [/latex] b) [latex]0,2 sqrt{20} [/latex] = [latex] sqrt{20*0,04} [/latex] = [latex] sqrt{0,8} [/latex] c) [latex] frac{1}{3} sqrt{18} [/latex] = [latex] sqrt{18* frac{1}{9} } [/latex] = [latex] sqrt{2}[/latex] d) [latex] frac{3}{4} sqrt{8} [/latex] = [latex] sqrt{8* frac{9}{16} } [/latex] = [latex] sqrt{ frac{9}{2} [/latex] e) [latex]1,2 sqrt{10} [/latex] = [latex] sqrt{10*1,44} [/latex] = [latex] sqrt{14,4} [/latex] 3. a) [latex] sqrt{63} [/latex] = [latex] sqrt{9*7} [/latex] = [latex]3 sqrt{7} [/latex] b) [latex] sqrt{80} [/latex] = [latex] sqrt{16*5} [/latex] = [latex]4 sqrt{5}[/latex] c) [latex] sqrt{132} [/latex] = [latex] sqrt{4*33} [/latex] = [latex]2 sqrt{33}[/latex] d) [latex] sqrt{98} [/latex] = [latex] sqrt{4*17} [/latex] = [latex]2 sqrt{17} [/latex] e) [latex] sqrt{279} [/latex] = [latex] sqrt{9*31} [/latex] = [latex]3 sqrt{31} [/latex] f) [latex] sqrt{605} [/latex] = [latex] sqrt{121*5} [/latex] = [latex]11 sqrt{5} [/latex] g) [latex] sqrt{405} [/latex] = [latex] sqrt{81*5} [/latex] = [latex]9 sqrt{5} [/latex] h) [latex] sqrt{847} [/latex] = [latex] sqrt{121*7} [/latex] = [latex]11 sqrt{7} [/latex] i) [latex] sqrt{1014} [/latex] = [latex] sqrt{169*6} [/latex] = [latex]13 sqrt{6}[/latex] j) [latex] sqrt{1152} [/latex] = [latex] sqrt{576*2} [/latex] = [latex]24 sqrt{2} [/latex] 4. a) [latex] sqrt{20} [/latex] = [latex] frac{2}{3} sqrt{45} [/latex] b) [latex] sqrt{7} [/latex] = [latex]0,2 sqrt{175} [/latex] c) [latex] sqrt{18} [/latex] = [latex]2 sqrt{4,5} [/latex] d) [latex] sqrt{18} [/latex] = [latex]1,5 sqrt{8} [/latex] e) [latex] sqrt{ frac{4}{3}[/latex] = [latex] frac{1}{3} * sqrt{12} [/latex] f) [latex] sqrt{2,4} [/latex] = [latex] frac{2}{5} * sqrt{15} [/latex] 5. a) liczba y, ponieważ = [latex]11 sqrt{3} [/latex], a liczby x i z = [latex]12 sqrt{2} [/latex] b) liczba y, ponieważ = [latex]-11 sqrt{3} [/latex], a liczby x i z = [latex]-5 sqrt{3} [/latex] 6. a) [latex] sqrt{2} * sqrt{3} * sqrt{6} [/latex] = [latex] sqrt{2*3*6} [/latex] = [latex] sqrt{36} [/latex] = [latex]6[/latex] b) [latex] sqrt{0,3} * sqrt{0,5} * sqrt{0,15} [/latex] = [latex] sqrt{0,3*0,5*0,15} [/latex] = [latex] sqrt{ frac{9}{400}[/latex] = [latex] frac{3}{20} [/latex] c) [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} [/latex] = [latex]3[/latex] d)[latex]( sqrt{50} : sqrt{54} )* sqrt{3} [/latex] = [latex] sqrt{50:54} * sqrt{3} [/latex] = [latex] sqrt{ frac{25}{27}}* sqrt{3} [/latex][latex] sqrt{ frac{25}{27}* 3} [/latex][latex] sqrt{ frac{25}{9}[/latex] = [latex] frac{5}{3} [/latex] e) [latex] sqrt{5 frac{9}{27}} : sqrt{1 frac{3}{9}[/latex] = [latex] sqrt{5 frac{9}{27} :1 frac{3}{9}[/latex] = [latex] sqrt{4} [/latex] = [latex]2[/latex] f) [latex] sqrt{6 frac{2}{3}} : sqrt{2,4} [/latex] = [latex] sqrt{2 frac{2}{3} :2,4} [/latex] = [latex] sqrt{ frac{25}{9}} [/latex] = [latex] frac{5}{3} [/latex] 7. a) [latex](3 sqrt{2}+ sqrt{18} -2 sqrt{8} )* sqrt{2} [/latex] = [latex]2 sqrt{2} * sqrt{2} [/latex] = [latex]4[/latex] b) [latex]( sqrt{24} -4 sqrt{3}+2 sqrt{12})* sqrt{6} [/latex] = [latex]2 sqrt{6} * sqrt{6} [/latex] = [latex]12[/latex] c) [latex](16 sqrt{2}-2 sqrt{32}+2 sqrt{72}) : sqrt{8} [/latex] = [latex]20 sqrt{2} : sqrt{8} [/latex] = [latex]10[/latex] d) [latex](5 sqrt{96}+4 sqrt{24}-3 sqrt{216}):2 sqrt{6} [/latex] = [latex]10 sqrt{6} :2 sqrt{6}[/latex] = [latex]5[/latex] 8. a) [latex]( sqrt{240} +3 sqrt{60} - sqrt{135})*2 sqrt{3} [/latex] = [latex]7 sqrt{15} *2 sqrt{3} [/latex] = [latex]42 sqrt{5} [/latex] b) [latex](11 sqrt{6} + sqrt{96} - sqrt{150}) :3 sqrt{2} [/latex] = [latex]10 sqrt{6} :3 sqrt{2} [/latex] = [latex] frac{10 sqrt{3} }{3} [/latex] 9. a) [latex](4-2 sqrt{5})*( sqrt{5} +3) = 4 sqrt{5} +12-10-6 sqrt{5} =-2 sqrt{5} +2[/latex] b) [latex](2 sqrt{6} +6)*( 2sqrt{3} -3 sqrt{2} )= 4 sqrt{18} -6 sqrt{12}+12 sqrt{3} -18 sqrt{2} =-6 sqrt{2} [/latex] c) [latex](9-2 sqrt{15})*(3 sqrt{3} +2 sqrt{5})= 27 sqrt{3} +18 sqrt{5} -6 sqrt{45}-4 sqrt{75} =7 sqrt{3} [/latex] d) [latex](2 sqrt{5}- sqrt{2})*( sqrt{10}+3) = 2 sqrt{50}+6 sqrt{5} - sqrt{20} -3 sqrt{2} =4 sqrt{5} +7 sqrt{2}[/latex]
Bardzo proszę o szybkie rozwiązanie tych zadań , mam z nimi problem a pilnie ich potrzebuję :)
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