Odpowiedź:
zad13
a)[tex]\sqrt{2} *\sqrt{6} =\sqrt{2*6} =\sqrt{12} =\sqrt{4*3} =2\sqrt{3} [/tex]
b)[tex]2\sqrt{3}* \sqrt{18} =2\sqrt{3*18} =2\sqrt{54} =2\sqrt{9*6} =2*3\sqrt{6} =6\sqrt{6} [/tex]
c)[tex]7\sqrt{10} *\frac{1}{2} \sqrt{5} =7*\frac{1}{2} *\sqrt{10*5} =\frac{7}{2} *\sqrt{50} =\frac{7}{2} *5\sqrt{2} =\frac{35}{2} \sqrt{2}=17\frac{1}{2} \sqrt{2} [/tex]
d)[tex]\sqrt{50}+\sqrt{2} =5\sqrt{2} +\sqrt{2} =6\sqrt{2} [/tex]
e)[tex]\sqrt{300} -2\sqrt{3} =10\sqrt{3} -2\sqrt{3} =8\sqrt{3} [/tex]
f)[tex]-2\sqrt{32} -2\sqrt{8} =-2*4\sqrt{2} -2*2\sqrt{2} =-8\sqrt{2}-4\sqrt{2} =-12\sqrt{2} [/tex]
zad14
a)[tex]\sqrt{2}*\sqrt{4\frac{1}{2} }=\sqrt{2*\frac{9}{2} } =\sqrt{9} =3[/tex]
b)[tex]\sqrt{2\frac{2}{3} } :\sqrt{\frac{2}{3} } =\sqrt{\frac{8}{3}*\frac{3}{2} } =\sqrt{4} =2[/tex]
c)[tex]\sqrt{6,4} :\sqrt{10} =\sqrt{\frac{64}{10} *\frac{1}{10} } =\sqrt{0,64} =0,8[/tex]
d)[tex]\sqrt[3]{10} *\sqrt[3]{0,1} =\sqrt[3]{10*0,1} =\sqrt[3]{1} =1[/tex]
e)[tex]\sqrt[3]{2\frac{2}{3} }* \sqrt[3]{\frac{1}{9} } =\sqrt[3]{\frac{8}{3}*\frac{1}{9} } =\sqrt[3]{\frac{8}{27} } =\frac{2}{3} [/tex]
f)[tex]\frac{\sqrt[3]{2,7} }{\sqrt[3]{100} } =\sqrt[3]{\frac{27}{10}*\frac{1}{100} } =\sqrt[3]{\frac{27}{1000} } =\frac{3}{10} =0,3[/tex]
g)[tex]\sqrt[3]{-9} *\sqrt[3]{3} =\sqrt[3]{-9*3} =\sqrt[3]{-27} =-3[/tex]
h)[tex]\frac{\sqrt[3]{128} }{\sqrt[3]{-2} } =\sqrt[3]{\frac{128}{-2} } =\sqrt[3]{-64} =-4[/tex]
i)[tex]\frac{\sqrt[3]{-0,5}*\sqrt[3]{4} }{\sqrt[3]{16} } =\sqrt[3]{\frac{-0,5*4}{16} } =\sqrt[3]{-\frac{1}{8} } =-\frac{1}{2} [/tex]
zad15
a)[tex]3\sqrt{2} >2\sqrt{2} [/tex]
b)[tex]\frac{\sqrt{6} }{6} >\frac{\sqrt{7} }{7} [/tex]
c)[tex]\frac{4}{5} \sqrt{10} >\frac{4}{5}\sqrt{13} [/tex]
Szczegółowe wyjaśnienie: