←Vrati se na zadatke2. ZadatakRacionaliziraj i skrati razlomak: 9+224+162.\frac{9+2\sqrt{2}}{4+\sqrt{162}}.4+1629+22.RješenjeVrijedi 9+224+162=9+224+92==9+224+92⋅4−924−92==36−812+82−3616−162==−732−146==22.\begin{aligned} \frac{9+2\sqrt{2}}{4+\sqrt{162}}&=\frac{9+2\sqrt{2}}{4+9\sqrt{2}}=\\ &=\frac{9+2\sqrt{2}}{4+9\sqrt{2}}\cdot\frac{4-9\sqrt{2}}{4-9\sqrt{2}}=\\ &=\frac{36-81\sqrt{2}+8\sqrt{2}-36}{16-162}=\\ &=\frac{-73\sqrt{2}}{-146}=\\ &=\frac{\sqrt{2}}{2}. \end{aligned}4+1629+22=4+929+22==4+929+22⋅4−924−92==16−16236−812+82−36==−146−732==22.
