sqrt(3+sqrt(5))-sqrt(3-sqrt(5))

Thank you, Melody

So we have

√(3 +√5) - √(3 -√5)

Let   √(3 +√5) - √(3 -√5)  =  x   = √(x^2)

So we have

√ [√(3 +√5) - √(3 -√5)]^2 =

√ [3 + √5 - 2√(3 +√5)√(3 -√5)+ 3 -√5 ] =

√ [3 - 2√(9-5) + 3] =

√ [6 -2√4] =

√ [6 - 2*2] =

√(6-4) =

√2

P.S.   -  That was a neat little trick I learned from another member......heureka .....!!!

Thanks, heureka !!!

tnx man! 

Thank you CPhill

Yes, i learned this trick from Heureka too.  It really is neat.  Thanks Heureka