Răspuns:
[tex]\boldsymbol{ \red{ \dfrac{7}{2} }}[/tex]
Explicație pas cu pas:
Raționalizăm numitorii
[tex]\sqrt{8} = \sqrt{2^2 \cdot 2} = 2\sqrt{2}[/tex]
[tex]\bigg(\dfrac{^{\sqrt{2}) } 2}{\sqrt{2}} + \dfrac{^{\sqrt{8} )} 3}{\sqrt{8}}\bigg) \cdot(\sqrt{8} - \sqrt{2}) = \bigg(\dfrac{^{4)} 2\sqrt{2}}{2} + \dfrac{3\sqrt{8}}{8}\bigg) \cdot(2\sqrt{2} - \sqrt{2}) = \\[/tex]
[tex]= \dfrac{8\sqrt{2} + 3\cdot2\sqrt{2}}{8} \cdot \sqrt{2} = \dfrac{8\sqrt{2} + 6\sqrt{2}}{8} \cdot \sqrt{2} = \dfrac{14\sqrt{2}}{8}^{(2} \cdot \sqrt{2} = \dfrac{7 \cdot 2}{4}^{(2} \\[/tex]
[tex]= \bf \dfrac{7}{2}[/tex]
