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sqrt(33+sqrt(8))sqrt(6+sqrt(3+sqrt(8)))sqrt(3+sqrt(3+sqrt(3+sqrt(8))))sqrt(3-sqrt(3+sqrt(3+sqrt(8))))

 Sep 23, 2017
 #1
avatar+2421 
+1

\(\sqrt{33+\sqrt{8}}*\sqrt{6+\sqrt{3+\sqrt{8}}}*\sqrt{3+\sqrt{3+\sqrt{3+\sqrt{8}}}}*\sqrt{3-\sqrt{3+\sqrt{3+\sqrt{8}}}}\approx32.87856\)

 

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 Sep 23, 2017
edited by TheXSquaredFactor  Sep 23, 2017
 #2
avatar+890 
+2

Work from the back to the front, three applications of the difference between two squares leads you to sqrt(33^2 - 8).

 Sep 23, 2017
 #3
avatar+110206 
+1

I just did this in great detail and then lost it all :(

Guest's answer is correct.  :)

 Sep 23, 2017

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