Verify that the quantities on both sides of the equation agree.
sqrt(6) + sqrt(2) = 2*sqrt{2 + sqrt(3)}
$\displaystyle \sqrt{6} + \sqrt{2} = 2 \sqrt{2 + \sqrt{3}}$
Obviously we want to get rid of that double square root on the RHS. So square both sides, as was suggested by MINOANMAN:
$\displaystyle \left ( \sqrt{6} + \sqrt{2}\right )^2 = \left ( 2 \sqrt{2 + \sqrt{3}} \right )^2$
$\displaystyle \left ( \sqrt{6} + \sqrt{2}\right )^2 = 2^2 ( 2 + \sqrt{3} )$
Can you expand out the LHS?
-Dan
Yes, I can expand the left side.
[sqrt(6)+sqrt(2)]^2
[sqrt(6)+sqrt(2)]* [sqrt(6)+sqrt(2)]
Applying the FOIL method and simplifying, I get:
8 + 4(sqrt{3}) on the left side which equals the right side.
Thus, both sides of the radical equation are in total agreement. Thanks again.