Write answer with only one root

[fhs1989]

Homework Statement

At the end I get the answer: sqrt(sqrt(3)+2)

It can be show that it is ( sqrt(6)+sqrt(2) ) / 2

How do I show this?, I have tried, to attempt it my manipulating the expression, but I can't seem to manage it.

 

[stgermaine]

((sqrt(6)+sqrt(2)) / 2)^2 = (1/4)(6+2*sqrt(2)*sqrt(6) + 2) = (1/4)(8 + 2sqrt(12)) = 1/4(8 + 4sqrt(3)) = sqrt(3) + 2