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How to simplyfy a square root term? Phonon dispersion relati

  1. Feb 20, 2015 #1
    I'm having trouble simplyfying this, I guess there's a trick but for the life of me cant remember what it is. Here is what I have so far:

    ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}##

    so I divide through by

    ##(\frac{1}{m}+\frac{1}{M}) ##

    to give

    ##\frac{\omega ^{2}}{\frac{1}{m}+\frac{1}{M}} = f-f (\frac{4q^{2} a^{2}}{mM}(\frac{1}{m}+\frac{1}{M})^{-2})^{\frac{1}{2}}##

    but now what? how would i simplyfy this further? here is the answer we have been given:

    BTIWt5B.jpg

    as you can see the square root has gone and there's a factor of 1/2 now inside the bracket, unclear of how he's simplyfied the square root term.

    here's the complete question in line with forums rules:

    PhanXsz.jpg

    thanks in advance for any help.
     
  2. jcsd
  3. Feb 20, 2015 #2
    doesnt matter im pretty sure he's used binomial theorem, mods please feel free to delete!
     
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