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Simplify each of this following surd

  1. Aug 8, 2015 #1
    1. The problem statement, all variables and given/known data
    3∜2 - ∜(2/81) + ∜32 - ∜162

    2. Relevant equations


    3. The attempt at a solution
    3∜2 - ∜(2/81) - ∜130
    3∜2 – ∜2/3 - ∜130
    exactly when i tried to calculate, i got problem with the next of this calculating, i confused. Can anybody help me for do the next of this calculating??
     
  2. jcsd
  3. Aug 8, 2015 #2

    mfb

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    Staff: Mentor

    Where does the 130 come from? That looks like an incorrect transformation.

    Did you split the numbers in the square roots into their prime factors?
     
  4. Aug 8, 2015 #3
    oh i wrong, i mean 3∜2 - ∜(2/81) - ∜130
    3∜2 – ∜2/3 - ∜130, and then the 130 come from 32-162
     
  5. Aug 8, 2015 #4

    Mark44

    Staff: Mentor

    First off, 32 - 162 = -130. More importantly, ##\sqrt[4]{a} - \sqrt[4]{b} \ne \sqrt[4]{a - b}##.
    As already mentioned simpligy ##\sqrt[4]{162}## by factoring 162 into its prime factors.
     
  6. Aug 8, 2015 #5
    ok, but how to solve ∜(2/81)?
     
  7. Aug 8, 2015 #6

    mfb

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    That part was right. $$ \frac{\sqrt[4]2}{3}$$
     
  8. Aug 8, 2015 #7

    HallsofIvy

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    Science Advisor

    It helps to know that [itex]81= 3^4[/itex] and [itex]162= 2(3^4)[/itex].
     
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