Simplify the following expression to a simplified fraction: \(\sqrt{\dfrac{\dfrac{5}{\sqrt{80}}+\dfrac{\sqrt{845}}{9}+\sqrt{45}}{\sqrt5}}\)
+6248 \(\text{well I guess I'd simplify it all to see if anything cancels}\\ \dfrac{5}{\sqrt{80}} = \dfrac{5\sqrt{80}}{80} = \dfrac{\sqrt{5}}{4}\\ \dfrac{\sqrt{845}}{9} = \dfrac{13\sqrt{5}}{9}\\ \sqrt{45}= 3\sqrt{5}\)
so we've got
\(\sqrt{\dfrac{\frac{\sqrt{5}}{4}+\frac{13\sqrt{5}}{9}+3\sqrt{5}}{\sqrt{5}}} = \\ \sqrt{\dfrac 1 4 + \dfrac{13}{9} + 3}=\\ \sqrt{\dfrac{9+52+108}{36}} = \sqrt{\dfrac{169}{36}}= \dfrac{13}{6}\)
