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geerky42 (geerky42):

I discovered that \(\sqrt{\dfrac{3+\sqrt{5}}{8}} = \dfrac{1+\sqrt{5}}{4}\) Can anyone prove me that this is true? I don't see how this is true.

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OpenStudy (anonymous):

Working with the RHS: \[\begin{align*}\frac{1+\sqrt5}{4}&=\sqrt\frac{(1+\sqrt5)^2}{16}\\ &=\sqrt{\frac{1+2\sqrt5+5}{16}}\\ &=\sqrt{\frac{6+2\sqrt5}{16}}\\ &=\sqrt{\frac{3+\sqrt5}{8}} \end{align*}\]

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