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Simplify the following expression to a simplified fraction: ​\(\sqrt{\dfrac{\dfrac{5}{\sqrt{80}}+\dfrac{\sqrt{845}}{9}+\sqrt{45}}{\sqrt5}}\)

 Feb 17, 2019
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\(\text{well I guess I'd simplify it all to see if anything cancels}\\ \dfrac{5}{\sqrt{80}} = \dfrac{5\sqrt{80}}{80} = \dfrac{\sqrt{5}}{4}\\ \dfrac{\sqrt{845}}{9} = \dfrac{13\sqrt{5}}{9}\\ \sqrt{45}= 3\sqrt{5}\)

 

so we've got

 

\(\sqrt{\dfrac{\frac{\sqrt{5}}{4}+\frac{13\sqrt{5}}{9}+3\sqrt{5}}{\sqrt{5}}} = \\ \sqrt{\dfrac 1 4 + \dfrac{13}{9} + 3}=\\ \sqrt{\dfrac{9+52+108}{36}} = \sqrt{\dfrac{169}{36}}= \dfrac{13}{6}\)

.
 Feb 17, 2019

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