Evaluate this... ?

Please evaluate the following :

#(2 + sqrt3)/ (sqrt2 + sqrt(2 + sqrt3))# + #(2 - sqrt3)/ (sqrt2 - sqrt(2 - sqrt3))#

1 Answer
iceman
May 4, 2018

#sqrt2#

Explanation:

#(2+sqrt3)/[sqrt2+sqrt(2+sqrt3)]+(2-sqrt3)/[sqrt2-sqrt(2-sqrt3)]#

#={(2+sqrt3)[sqrt2-sqrt(2-sqrt3)]}/{[sqrt2+sqrt(2+sqrt3)][sqrt2-sqrt(2-sqrt3)]}+{(2-sqrt3)[sqrt2+sqrt(2+sqrt3)]}/{[sqrt2+sqrt(2+sqrt3)][sqrt2-sqrt(2-sqrt3)]}#

#=sqrt(3 (2 + sqrt(3)))/3+sqrt(3 (2 - sqrt(3)))/3#

#={sqrt(3 (2 + sqrt(3)))+sqrt(3 (2 - sqrt(3)))}/3#

#={sqrt(3) [sqrt(2 + sqrt(3)) +sqrt(2 - sqrt(3))]}/3#

#=(3sqrt2)/3#

#=sqrt2#

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