[tex]a)\\{}\quad\dfrac2{\sqrt{10}}\cdot\dfrac{\sqrt{10}}{\sqrt{10}}= \dfrac{2\sqrt{10}}{10}= \dfrac{\sqrt{10}}5\\\\\\b)\\{}\quad\dfrac{16}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}= \dfrac{16\sqrt2}2= 8\sqrt2\\\\\\c)\\{}\quad\dfrac{3+\sqrt3}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}= \dfrac{3\sqrt3+3}{3}= \dfrac{3(\sqrt3+1)}3= \dfrac{\sqrt3+1}1=\sqrt3+1\\\\\\d)\\{}\quad\dfrac1{4\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}= \dfrac{\sqrt2}{4\cdot2}= \dfrac{\sqrt2}8[/tex]
