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Simplifying square root of an irrational

  1. Jan 5, 2016 #1
    1. The problem statement, all variables and given/known data
    Find [(3 - 51/2)/2]1/2

    2. Relevant equations


    3. The attempt at a solution
    My calculator says (-1 + √5)/2
    I have no idea how. Rationalising doesn't really do much good. Just tell me where to start.
     
  2. jcsd
  3. Jan 5, 2016 #2

    blue_leaf77

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    Multiplying the original expression with ##\sqrt{2}/\sqrt{2}## will give you ##\sqrt{6-2\sqrt{5}}## in the numerator. Then think of the terms under the radical as having the form of ##(a-b)^2 = a^2-2ab+b^2##.
     
  4. Jan 5, 2016 #3
    Could you please elaborate? I'm not getting anywhere. I assume you mean use something like completing the square but I can't do it.
     
  5. Jan 5, 2016 #4

    blue_leaf77

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    What do you get after multiplying the original expression with ##\frac{\sqrt{2}}{\sqrt{2}}##?
     
  6. Jan 5, 2016 #5

    vela

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    You could also try working the other direction. Find the square of ##\frac{-1 + \sqrt 5}{2}## and see how it simplifies.
     
  7. Jan 5, 2016 #6
    Oh I got that, ie √(6-2√5) ÷ 2
    I don't get what I'm supposed to do after this.
     
  8. Jan 5, 2016 #7

    blue_leaf77

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    It is √(6-2√5) ÷ 2. Then express the terms under the radical in the form I wrote in post #2, that is, write ##6-2√5 = a^2+b^2-2ab## . FInd the right pair of ##a## and ##b## such that the LHS is equal to RHS.
     
  9. Jan 5, 2016 #8
    Got it! Thanks!
     
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