[latex]1.\ a)3^{frac{1}{2}}*12^{frac{1}{2}}+5^{frac{1}{3}}*25^{frac{1}{3}}=(3*12)^{frac{1}{2}}+(5*25)^{frac{1}{3}}=\sqrt{36}+sqrt[3]{125}=6+5=underline{11}\ c)frac{5*4^{7}-6*16^3}{2^{13}}=frac{5*2^{14}-6*2^{12}}{2^{13}} =frac{2^{12}(5*2^2-6)}{2^{13}}=frac{5*2^2-6}{2}=frac{14}{2}=underline{7}\ d)sqrt{17+2sqrt{2}*sqrt{8}}=sqrt{17+2sqrt{2*8}}=sqrt{17+2sqrt{16}}\ =sqrt{17+2*4}=sqrt{25}=underline{5}\ e)sqrt{140-sqrt{361}}=sqrt{140-19}=sqrt{121}=underline{11}[/latex] [latex]2.\ b)frac{4sqrt{3}-12sqrt{2}}{sqrt{6}}*frac{sqrt{6}}{sqrt{6}}=frac{sqrt{6}(4sqrt{3}-12sqrt{2})}{6}=frac{4sqrt{18}-12sqrt{12}}{6}=frac{4(3sqrt{2}-3*2sqrt{3})}{6}\ =frac{12sqrt{2}-24sqrt{3}}{6}=frac{6(2sqrt{2}-4sqrt{3})}{6}=underline{2(sqrt{2}-2sqrt{3}})}\ c)frac{6}{3sqrt{2}-4}*frac{3sqrt{2}+4}{3sqrt{2}+4}=frac{6(3sqrt{2}+4)}{18-16}=frac{18sqrt{2}+24}{2}=underline{9sqrt{2}+12}[/latex] [latex]3.\ a)Liczby naturalne:0;sqrt{16};1000\ b)Liczby calkowite:0;sqrt{16};1000;-4;-25;-1\ c)Liczby wymierne:0;sqrt{16};1000;-4;-25;-1;frac{18}{5};-4,(51);-10frac{3}{4}\ d)Liczby niewymierne:sqrt{5};9,1568425...\ [/latex] [latex]4.\ (4x-1)^2-(3+4x)(3-4x)=16x^2-8x+1-(9-16x^2)=\ =16x^2-8x+1-9+16x^2=32x^2-8x-8\ x=frac{1}{2}\ (4*0,5-1)^2-(3+4*0,5)(3-4*0,5)=1-(5)=-4[/latex]
