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Simplifying radical equations

  1. Apr 18, 2004 #1
    Simplify
    sqrt(11+sqrt72)) + sqrt(11-sqrt(72))

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    I don't know where to begin for this one, but apparently my calculator says the answer is 6 :redface:
     
  2. jcsd
  3. Apr 18, 2004 #2

    matt grime

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    let x be the surd, square x, what do you get?
     
  4. Apr 18, 2004 #3
    let x be the "surd"?
     
  5. Apr 18, 2004 #4
    ok, set sqrt(11+sqrt72)) + sqrt(11-sqrt(72)) = x
    (by the way, sqrt(72) = 6*sqrt(2), which i'll just call 6r2 for simplicity)
    square both sides, we get
    (sqrt(11+sqrt72)) + sqrt(11-sqrt(72)))^2 = x^2
    simplify and you get
    11+6r2+2*sqrt((11+6r2)(11-6r2))+11-6r2=x^2
    22+2sqrt(121+11*6r2-11*6r2-36*2)=x^2
    22+2*sqrt(121-72)=x^2
    22+2*sqrt(49)=x^2
    22+2*7=x^2
    36=x^2
    x=6 (well, plus or minus, but we know it must be positive since the addition of two non-complex roots must be >= 0)
     
  6. Apr 18, 2004 #5

    matt grime

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    Yes, surd: an expression involving radicals. I just didn't want to have to type it out. Just square the expression, simplify and take the square root, et voila, we have 6, with the appropriate choice of sign.
     
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