[tex]\dfrac{\sqrt{8} }{\sqrt{45}\cdot\sqrt{2} } =\dfrac{\sqrt{4\cdot2} }{\sqrt{9\cdot5}\cdot\sqrt{2} } =\dfrac{\sqrt{4} \cdot\sqrt{\not2} }{\sqrt{9}\cdot\sqrt{5}\cdot\sqrt{\not2} } =[/tex]
[tex]=\dfrac{\sqrt{2^{2}} }{\sqrt{3^{2}}\cdot\sqrt{5} }=\dfrac{2}{3\cdot\sqrt{5} } \cdot\dfrac{\sqrt{5} }{\sqrt{5} } =\dfrac{2\cdot\sqrt{5} }{3\cdot5}=\dfrac{2\sqrt{5} }{15}[/tex]
