Răspuns :

Triunghiul1id

[tex]\frac{1}{\sqrt{2} } +\frac{2}{\sqrt{8} } +\frac{3}{\sqrt{18} } =\frac{1}{\sqrt{2} } +\frac{2}{2\sqrt{2} } ^{(2}+\frac{3}{3\sqrt{2} } ^{(3}=\frac{1}{\sqrt{2} } +\frac{1}{\sqrt{2} } +\frac{1}{\sqrt{2} } =\frac{3}{\sqrt{2} } |\cdot \sqrt{2} =\frac{3\sqrt{2} }{2}[/tex]

[tex]\frac{6}{\sqrt{3} } -\frac{8}{\sqrt{12} } +\frac{9}{\sqrt{27} } =\frac{6}{\sqrt{3} } -\frac{8}{2\sqrt{3} } ^{(2}+\frac{9}{3\sqrt{3} } ^{(3}=\frac{6}{\sqrt{3} } -\frac{4}{\sqrt{3} } +\frac{3}{\sqrt{3} }=\frac{5}{\sqrt{3}} |\cdot \sqrt{3} =\frac{5\sqrt{3} }{3}[/tex]

[tex](\frac{1}{\sqrt{5} } -\frac{1}{\sqrt{20} } +\frac{1}{\sqrt{45} } -\frac{1}{\sqrt{125} } )\cdot (2-\frac{1}{38} )=[/tex]

[tex](^{30)}\frac{1}{\sqrt{5} } -^{15)}\frac{1}{2\sqrt{5} } +^{10)}\frac{1}{3\sqrt{5} } -^{6)}\frac{1}{5\sqrt{5} } )\cdot (\frac{76}{38} -\frac{1}{38} )=[/tex]

[tex](\frac{30}{30\sqrt{5} } -\frac{15}{30\sqrt{5} } +\frac{10}{30\sqrt{5} } -\frac{6}{30\sqrt{5} } )\cdot \frac{75}{38} =[/tex]

[tex]\frac{30-15+10-6}{30\sqrt{5} } \cdot \frac{75}{38} =\frac{19}{30\sqrt{5} } \cdot \frac{75}{38} =\frac{1}{2\sqrt{5} } \cdot \frac{5}{2} =\frac{5}{4\sqrt{5} } |\cdot \sqrt{5} =\frac{\sqrt{5} }{4}[/tex]

[tex](\sqrt{54} -^{\sqrt{6})} \frac{6}{\sqrt{6} } )\cdot (\frac{48}{\sqrt{6} } -\frac{15}{\sqrt{24} } )=(3\sqrt{6} -\frac{6\sqrt{6} }{6} ^{(6})\cdot (^{2)}\frac{48}{\sqrt{6} } -\frac{15}{2\sqrt{6} })=[/tex]

[tex]=(3\sqrt{6} -\sqrt{6} )\cdot (\frac{96}{2\sqrt{6}}-\frac{15}{2\sqrt{6} } )=2\sqrt{6} \cdot \frac{81}{2\sqrt{6} } =81[/tex]

Dariusbarbuid

Răspuns:

  • [tex] \frac{3 \sqrt{2} }{2} [/tex]
  • [tex] \frac{5 \sqrt{3} }{3} [/tex]
  • √5/4
  • [tex]81[/tex]

Explicație pas cu pas:

[tex]a) \: \frac{1}{ \sqrt{2} } + \frac{2}{ \sqrt{8} } + \frac{3}{ \sqrt{18} } = [/tex]

[tex] \frac{ \sqrt{2} }{2} + \frac{2}{ 2\sqrt{2} } + \frac{3}{3 \sqrt{2} } = [/tex]

[tex] \frac{ \sqrt{2} }{2} + \frac{1}{ \sqrt{2} } + \frac{1}{ \sqrt{2} } = [/tex]

[tex] \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} + \frac{ \sqrt{2} }{2} = [/tex]

[tex] \frac{ \sqrt{2} + \sqrt{2} + \sqrt{2} }{2} = [/tex]

[tex] \frac{3 \sqrt{2} }{2} [/tex]

[tex]b) \: \frac{6}{ \sqrt{3} } - \frac{8}{ \sqrt{12} } + \frac{9}{ \sqrt{27} } = [/tex]

[tex]2 \sqrt{3} - \frac{8}{2 \sqrt{3} } + \frac{9}{3 \sqrt{3} } = [/tex]

[tex]2 \sqrt{3} - \frac{4}{ \sqrt{3} } + \frac{3}{ \sqrt{3} } = [/tex]

[tex]2 \sqrt{3} - \frac{4 \sqrt{3} }{3} + \sqrt{3} = [/tex]

[tex] \frac{5 \sqrt{3} }{3} [/tex]

[tex]c) \: ( \frac{1}{ \sqrt{5} } - \frac{1}{ \sqrt{20} } + \frac{1}{ \sqrt{45} } - \frac{1}{ \sqrt{125} } ) \times (2 - \frac{1}{38} ) = [/tex]

[tex]( \frac{1}{ \sqrt{5} } - \frac{1}{2 \sqrt{5} } + \frac{1}{3 \sqrt{5} } - \frac{1}{5 \sqrt{5} } ) \times \frac{75}{38} = [/tex]

[tex] \frac{19}{30 \sqrt{5} } \times \frac{75}{38} = [/tex]

[tex] \frac{1}{2 \sqrt{5} } \times \frac{5}{2} = [/tex]

[tex] \frac{5}{4 \sqrt{5} } = [/tex]

[tex] \frac{ \sqrt{5} }{4} [/tex]

[tex]d) \: ( \sqrt{54} - \frac{6}{ \sqrt{6} } ) \times ( \frac{48}{ \sqrt{6} } - \frac{15}{ \sqrt{24} }) = [/tex]

[tex](3 \sqrt{6} - \sqrt{6} ) \times ( \frac{48}{ \sqrt{6} } - \frac{15}{2 \sqrt{6} } ) = [/tex]

[tex]2 \sqrt{6} \times \frac{81}{2 \sqrt{6} } = [/tex]

[tex]81[/tex]

ID Alte intrebari