Write answer with only one root

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SUMMARY

The discussion focuses on demonstrating the equivalence of the expression sqrt(sqrt(3)+2) to (sqrt(6)+sqrt(2))/2. The user successfully manipulates the latter expression by squaring it, leading to a simplified form that confirms the original statement. The key steps involve expanding the squared expression and simplifying it to match the left-hand side of the equation.

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Students studying algebra, mathematics enthusiasts, and anyone looking to improve their skills in manipulating and simplifying mathematical expressions.

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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.
 
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((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
 

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