Stage: 5 Challenge Level: 
The absurdity of it!
Find the exact values of $$\sqrt{2 + \sqrt 3}- \sqrt{2 - \sqrt3}$$ and of $$\root 3 \of {2 + \sqrt 5}+ \root 3 \of {2 - \sqrt 5}$$
alphas. Surds. Identities. epsilons. Manipulating algebraic expressions/formulae. Mathematical reasoning & proof. Inequality/inequalities. Stage 5 - Reviewed 2012. Powers & roots. Summation of series.
Published July 1999.
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