1. ## Radicals On Both Sides of Equation

Verify that the quantities on both sides of the equation agree.

sqrt(6) + sqrt(2) = 2*sqrt{2 + sqrt(3)}

2. ## Re: Radicals On Both Sides of Equation

rise to power 2 both sides and you will get it..it is easy

3. ## Re: Radicals On Both Sides of Equation

Can you demonstrate just how "easy" this can be done without using a calculator?

4. ## Re: Radicals On Both Sides of Equation

Originally Posted by nycmath
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

5. ## Re: Radicals On Both Sides of Equation

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.