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Math Help - Radicals On Both Sides of Equation

  1. #1
    Super Member nycmath's Avatar
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    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)}
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    Re: Radicals On Both Sides of Equation

    rise to power 2 both sides and you will get it..it is easy
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  3. #3
    Super Member nycmath's Avatar
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    Re: Radicals On Both Sides of Equation

    Can you demonstrate just how "easy" this can be done without using a calculator?
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    Forum Admin topsquark's Avatar
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    Re: Radicals On Both Sides of Equation

    Quote Originally Posted by nycmath View Post
    Verify that the quantities on both sides of the equation agree.

    sqrt(6) + sqrt(2) = 2*sqrt{2 + sqrt(3)}
    \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:
    \left ( \sqrt{6} + \sqrt{2}\right )^2 = \left ( 2 \sqrt{2 + \sqrt{3}} \right )^2

    \left ( \sqrt{6} + \sqrt{2}\right )^2 = 2^2 ( 2 + \sqrt{3} )

    Can you expand out the LHS?

    -Dan
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  5. #5
    Super Member nycmath's Avatar
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    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.
    Last edited by nycmath; October 21st 2013 at 04:36 PM.
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