a)

[tex]\dfrac{7}{\sqrt{2} }=\dfrac{7}{\sqrt{2} }\cdot \dfrac{\sqrt{2} }{\sqrt{2} }=\dfrac{7\sqrt{2} }{2}[/tex]

b)

[tex]\dfrac{\sqrt{2} }{3\sqrt{5}}=\dfrac{\sqrt{2} }{3\sqrt{5}}\cdot \dfrac{\sqrt{5} }{\sqrt{5}}=\dfrac{\sqrt{10}}{3\cdot 5}=\dfrac{\sqrt{10}}{15}[/tex]

c)

[tex]\dfrac{5}{7\sqrt{5} } =\dfrac{5}{7\sqrt{5} } \cdot \dfrac{\sqrt{5} }{\sqrt{5} }=\dfrac{5\sqrt{5} }{7\cdot 5}=\dfrac{\sqrt{5} }{7}[/tex]

d)

[tex]\dfrac{4}{\sqrt{6} } =\dfrac{4}{\sqrt{6} } \cdot \dfrac{\sqrt{6} }{\sqrt{6} }=\dfrac{4\sqrt{6} }{6}=\dfrac{2\sqrt{6} }{3}[/tex]