Răspuns: -8
Explicație pas cu pas:
[tex](\frac{3}{\sqrt{27} } - \frac{8}{\sqrt{12} } + \frac{5}{\sqrt{75} } )[/tex] ÷ [tex]\frac{\sqrt{3} }{12} =?[/tex]
Mai întâi simplificăm radicalii:
[tex]\sqrt{27} = 3\sqrt{3} \\\sqrt{12} = 2\sqrt{3}\\\sqrt{75} = 5\sqrt{3}[/tex]
Acum calculul devine:
[tex](\frac{3}{3\sqrt{3} } - \frac{8}{2\sqrt{3} } + \frac{5}{5\sqrt{3} } )[/tex] ÷[tex]\frac{\sqrt{3} }{12}[/tex]
Acum rationalizam fractiile:
[tex]\frac{3}{3\sqrt{3} } = \frac{1}{\sqrt{3} } = \frac{\sqrt{3} }{3} \\\frac{8}{2\sqrt{3} } = \frac{4}{\sqrt{3} } = \frac{4\sqrt{3} }{3} \\\frac{5}{5\sqrt{3} } = \frac{1}{\sqrt{3} } = \frac{\sqrt{3} }{3}[/tex]
(Am simplificat 3 cu 3, 8 cu 2 si 5 cu 5)
[tex]\frac{\sqrt{3} }{3} - \frac{4\sqrt{3} }{3} + \frac{\sqrt{3} }{3} = \frac{\sqrt{3}-4\sqrt{3} +\sqrt{3} }{3} = \frac{2\sqrt{3}-4\sqrt{3} }{3} = \frac{-2\sqrt{3} }{3} = -\frac{2\sqrt{3} }{3}[/tex]
Asadar, am ajuns la calculul:
[tex]-\frac{2\sqrt{3} }{3}[/tex] ÷ [tex]\frac{\sqrt{3} }{12}[/tex]
Acum, deoarece este o impartire intre fractii, transformam in inmultire intre prima fractie si a doua fractie inversata:
[tex]-\frac{2\sqrt{3} }{3}[/tex] ÷ [tex]\frac{\sqrt{3} }{12} =[/tex] [tex]-\frac{2\sqrt{3} }{3}[/tex] × [tex]\frac{12}{\sqrt{3} }[/tex]
Simplificam [tex]\sqrt{3}[/tex] cu [tex]\sqrt{3}[/tex] si 12 cu 3:
[tex]-\frac{2}{1}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]-2[/tex] × [tex]4[/tex][tex]= -8[/tex]
In caz ca nu ai inteles, iti atasez si o fotografie.
Sper ca te-am ajutat!
