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Help with factor large numbers

  1. Mar 30, 2010 #1
    I am 31 and just started back in Math. My first class is Intermediate Algebra. I am sloving equations that force me to factor large numbers. Not sure if this is a skill that I was supposed to rember from high school, but nevertheless it is taking me a long time to do so. Can anyone tell me what the rules are when factor large roots. For example

    1. w + 14 = 1458 to the 4th root.

    Thanks for any advice.

    EG
     
  2. jcsd
  3. Mar 30, 2010 #2

    Mark44

    Staff: Mentor

    Re: Factoring?

    I'm not sure what your equation is. Is it this?
    [tex]w + 14 = \sqrt[4]{1458}[/tex]

    Click on the equation I wrote to see the LaTeX script I wrote for this equation.

    If that's the equation you want to solve, there is no factoring needed. All you have to do to solve for w is to add -14 to both sides of the equation.
     
  4. Mar 30, 2010 #3
    Re: Factoring?

    Yes. How do you simplfy the square root?
     
  5. Mar 30, 2010 #4

    Mark44

    Staff: Mentor

    Re: Factoring?

    That's a fourth root.
    Simplify it by finding all factors and seeing if any are to the fourth or higher power. For this problem, 1458 = 2 * 729 = 2 * 9 * 81 = 2 * 93 = 2 * 36

    The last expression can also be written as 34 * 2 * 9 = 34 * 18

    Now use the property of square roots, cube roots, fourth roots, etc. that says
    [tex]\sqrt[n]{ab} = \sqrt[n]{a}\sqrt[n]{b}[/tex]

    For even roots (square root, fourth root, etc.) in the equation above, both a and b have to be nonnegative. For odd roots (cube root, fifth root, etc.) a and be can be any real numbers.
     
  6. Mar 30, 2010 #5
    Re: Factoring?

    I understand the rule but how you get to step two - 2 x 9 x 81
     
  7. Mar 30, 2010 #6

    Mark44

    Staff: Mentor

    Re: Factoring?

    729 = 9 * 81. I used the concept I mentioned to you in another thread - if the sum of the digits of a number is 9 or a multiple of 9, the number is divisible by 9.

    So 1458 = 2 * 729 = 2 * 9 * 81
     
  8. Mar 30, 2010 #7
    Re: Factoring?

    Thanks again both threads were a big help!!!

    EG:approve:
     
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