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Homework Help: Radical Simplification

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data
    I got this expression while solving a problem.

    sin(theta)=[√3+1-√(4-2√3)]/4
    Using calculator I got RHS=0.5
    How do we simplify it without using a calc?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 1, 2010 #2

    ehild

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    Try to write 4-2√3 as the square of (√3-a) . What is a?

    ehild
     
  4. Sep 1, 2010 #3

    HallsofIvy

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    ehild, did you intend that to be [itex]\sqrt{(3- a)}[/itex] or [itex](\sqrt{3})- a[/itex]?
     
  5. Sep 1, 2010 #4

    ehild

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    Naturally, √3 +a = 1.7320508.. +a. You have to perform a higher operation first, and square root is of higher order than addition or subtraction. So is multiplication to addition. 2*3+4 =10 and it is not the same as 2*(3+4)=14. Or 6/2+3=6, and not 6/(2+3)=1.2. √9+16=19 and it is not √(9+16)=5. The square of (√3-1) is (√3-1)^2 = 4-2√3 and not √3-1^2=√3-1. Or it is on the other way at other parts of the world?

    ehild
     
  6. Sep 2, 2010 #5

    Mentallic

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    Yes?

    Abdul Quadeer, [tex]a+b=\sqrt{(a+b)^2}[/tex], see if you can work some magic with this idea.
     
  7. Sep 2, 2010 #6
    Thanks, I got the answer.
    Mentallic- there is a slight error in your idea.
    LHS =|a+b|
     
  8. Sep 2, 2010 #7

    Mentallic

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    Haha yep :smile: I didn't want to complicate things by saying in the case that a+b>0 or anything like that. You know, the KISS principle. But I'm glad you were able to spot my simplification (in other words, the error, but I'm not willing to admit it :wink:)
     
  9. Sep 2, 2010 #8
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