Odpowiedź:
[tex]Zad.1.\\a) 3\sqrt{20} +\sqrt{5}=3*2\sqrt{5} +\sqrt{5} =6\sqrt{5} +\sqrt{5} =7\sqrt{5} \\b)\sqrt{90}+\sqrt{40} +\sqrt{250}=3\sqrt{10} +2\sqrt{10} +5\sqrt{10} =10\sqrt{10} \\c)\sqrt{18} -2\sqrt{8}=3\sqrt{2} -2*2\sqrt{2}=3\sqrt{2} -4\sqrt{2}=-\sqrt{2} \\d)\frac{\sqrt{50}+\sqrt{72} }{\sqrt{2} } =\frac{5\sqrt{2}+6\sqrt{2} }{\sqrt{2} } =\frac{11\sqrt{2} }{\sqrt{2} } =11\\\\[/tex]
[tex]Zad.2.\\a)\frac{3}{\sqrt{6} } =\frac{3}{\sqrt{6} } *\frac{\sqrt{6} }{\sqrt{6} } =\frac{3\sqrt{6} }{\sqrt{36} } =\frac{3\sqrt{6} }{6} =\frac{\sqrt{6} }{2}[/tex]
[tex]b)\frac{\sqrt{2} }{5\sqrt{7} } =\frac{\sqrt{2} }{5\sqrt{7} }*\frac{\sqrt{7} }{\sqrt{7} } =\frac{\sqrt{14} }{5*7} =\frac{\sqrt{14} }{35}[/tex]
[tex]c) \frac{5}{3\sqrt{10} } =\frac{5}{3\sqrt{10} } *\frac{\sqrt{10} }{\sqrt{10} } =\frac{5\sqrt{10} }{3*10} =\frac{5\sqrt{10} }{30} =\frac{\sqrt{10} }{6}[/tex]
[tex]d)\frac{\sqrt{3}-3 }{\sqrt{3} }=\frac{\sqrt{3}-3 }{\sqrt{3} } *\frac{\sqrt{3} }{\sqrt{3} } =\frac{3-3\sqrt{3} }{3} =\frac{1-\sqrt{3} }{1} =1-\sqrt{3}[/tex]
[tex]Zad.3.\\a)6\sqrt{28} +3\sqrt{63}=6*2\sqrt{7} +3*3\sqrt{7} =12\sqrt{7}+9\sqrt{7} =21\sqrt{7}[/tex]
[tex]b)5\sqrt{32} -2\sqrt{98} =5*4\sqrt{2} -2*7\sqrt{2} =20\sqrt{2} -14\sqrt{2}=6\sqrt{2} \\[/tex]
[tex]c)\frac{4}{\sqrt{2} } -\frac{2\sqrt{6} }{\sqrt{3} } =\frac{4}{\sqrt{2} } -2\sqrt{2}=\frac{4\sqrt{2} }{2} -2\sqrt{2} =2\sqrt{2} -2\sqrt{2} =0[/tex]
