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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