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calculati:
([tex] \sqrt{0.(3)} + \frac{2 \sqrt{3} }{3} ) \times \sqrt{3 } + ( \sqrt{0.(2)} + \frac{4}{3 \sqrt{2} } ) \times \sqrt{2} [/tex]


Răspuns :

 

[tex]\displaystyle\bf\\\left(\sqrt{0,\!(3)}+\frac{2\sqrt{3}}{3}\right)\times\sqrt{3}+\left(\sqrt{0,\!(2)}+\frac{4}{3\sqrt{2}}\right)\times\sqrt{2}=\\\\\\=\left(\sqrt{\frac{3}{9}}+\frac{2\sqrt{3}}{3}\right)\times\sqrt{3}+\left(\sqrt{\frac{2}{9} }+\frac{4\sqrt{2}}{3\times2}\right)\times\sqrt{2}=\\\\\\=\left(\frac{\sqrt{3}}{3}+\frac{2\sqrt{3}}{3}\right)\times\sqrt{3}+\left(\frac{\sqrt{2}}{3} +\frac{2\sqrt{2}}{3}\right)\times\sqrt{2}=[/tex]

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[tex]\displaystyle\bf\\=\left(\frac{\sqrt{3}+2\sqrt{3}}{3}\right)\times\sqrt{3}+\left(\frac{\sqrt{2}+2\sqrt{2}}{3}\right)\times\sqrt{2}=\\\\\\=\left(\frac{3\sqrt{3}}{3}\right)\times\sqrt{3}+\left(\frac{3\sqrt{2}}{3}\right)\times\sqrt{2}=\\\\\\=\sqrt{3}\times\sqrt{3}+\sqrt{2}\times\sqrt{2}=\\\\=3+2=\boxed{\bf5}[/tex]