Answer:
a) [tex]$\frac{\sqrt{15} }{\sqrt{5}}\cdot \frac{\sqrt{5} }{\sqrt{5}}=\frac{\sqrt{75} }{5}=\frac{5\sqrt{3}}{5}=\sqrt{3} $[/tex]
or simply
[tex]$\frac{\sqrt{15}}{\sqrt{5}}=\sqrt{\frac{15}{5}}=\sqrt{3}$[/tex]
b)[tex]$\frac{\sqrt{3}\:}{\sqrt{6}} \cdot \frac{\sqrt{6}\:}{\sqrt{6}}=\frac{\sqrt{18} }{6}=\frac{3\sqrt{2} }{6}=\frac{\sqrt{2} }{2} $[/tex]
or
[tex]$\frac{\sqrt{3}}{\sqrt{6}}=\sqrt{\frac{3}{6}}=\sqrt{\frac{1}{2}}$[/tex]
[tex]$\sqrt{\frac{1}{2}}=\frac{\sqrt{2} }{2} $[/tex]
