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Quantitative Reasoning Square Root Question

Discussion in 'DAT Discussions' started by ephesus32, Dec 29, 2008.

  1. ephesus32

    7+ Year Member

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    Hi,

    The fourth root of x^3 times the square root of x equals 32. what is x?

    Can somebody systematically take me to this? Thanks. I'm getting to point where it is X^(5/4)=32, but don't know how to get the answer easily after that. Thanks.


    The answer is 16.
     
  2. sciencegod

    sciencegod Super Member
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    problem is messed up. try it. plug 16 in for x its not 32.
     
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  3. OP
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    ephesus32

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    hmmmm.. I don't think it's messed up. Plugging in 16 works for me in the calculator. Try it again, I'm sure you'll get it.
     
  4. Sublimation

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    This is actually simple if you think SAT math. Look they drew it out like that so you get confused. remember that the square root of something is that thing ^.5. Just do the same thing here express the problem in a way that you can work it out as such

    4Roots of (x^3) is the same as saying X^(3/4)
    so multiply tat by X^(1/2) and you get

    X^(3/4) . X^(1/2) = X^[(3/4)+(1/2)] =32
    Then solve X^(5/4)=32

    32^4/5 is 16 =X
     
  5. OP
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    ephesus32

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    Thanks Sublimation.
    However, 32^(4/5) is kind of time consuming for the QC section doing it mathematically especially getting the fifth square root. Is there any better time efficient way to figure it out?
     
  6. Streetwolf

    Streetwolf Ultra Senior Member
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    Yeah. Know that the fifth root of 32 is 2. That should be something you remember.

    And even if you didn't know... it's the 5th root! Anything to the 5th power makes it a LOT bigger. And since 32 isn't exactly that large of a number, it makes sense that you should think that 2 is the 5th root.
     
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    #6 Streetwolf, Dec 30, 2008
    Last edited: Dec 30, 2008
  7. sciencegod

    sciencegod Super Member
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    streetwolf is mathgod.
     
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  8. joonkimdds

    joonkimdds Senior Member
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    can I be PATgod since science and math god are already assigned?:idea:
     
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    ephesus32

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    thanks streetwolf... that explains a lot
     

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