1. Zadatak

Racionalizacijom nazivnika u prva dva člana izraza dobivamo: $$\frac1{\sqrt7+\sqrt5}=\frac{\sqrt7-\sqrt5}{2}\quad\text{i}\quad\frac1{\sqrt5-\sqrt3}=\frac{\sqrt5+\sqrt3}{2}.$$ Nadalje, vrijedi $$\frac{\sqrt{1.5}-\sqrt{3.5}}{\sqrt2}=\frac{\sqrt{\frac32}-\sqrt{\frac72}}{\sqrt2}=\frac{\frac{\sqrt3-\sqrt7}{\sqrt2}}{\sqrt2}=\frac{\sqrt3-\sqrt7}{2}.$$ Konačno, $$\frac{\sqrt7-\sqrt5}{2}+\frac{\sqrt5+\sqrt3}{2}-\frac{\sqrt3-\sqrt7}{2}=\frac{2\sqrt7}{2}=\sqrt7.$$