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Reducing Radicals and Squares

  1. Apr 26, 2004 #1
    First I'd like to say that I'm getting back into college after several years out in the job market. Unfortunately, I need to complete several more upper division math courses before I can complete my CS degree. Before I go back and start taking my classes again, I've been trying to self-study my way back through Calc I, and having difficulty just getting beyond the first section. Maybe I just need to refamiliarize myself with the basics.

    What has me stuck is determining the distance between two points. Pretty simple. I understand the theory, and can work the problems well, until I got to this one, and I've been stuck.

    Determine the distance between two points:
    (1,√3), (-1,1)

    My book shows the answer as:

    (I'm at work, I'll need to verify this, but 99% sure this is what the book states. I do know the question is 100% correct.)

    When I apply the distance formula:

    I get:

    When I reduce this I get:

    Am I not reducing this far enough? If so, how do you reduce down to √(8-2√3)?

    Thanks for your help and patience!
  2. jcsd
  3. Apr 26, 2004 #2


    User Avatar

    Just calculate the square:


    = √(4+(1-√3)(1-√3))

    = √(4+1-2√3+3)

    = √(8-2√3)
    Last edited: Apr 26, 2004
  4. Apr 26, 2004 #3
    Thank you! Makes sense to me now. I know it seems basic, but I suppose this is where I have the most difficult time.. knowing where to use what to get the most simple answer.

    Thanks again for your help!
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