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Factor this expression

  1. Mar 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Express the following as A2+B2:

    3[√3+√5+√7]2

    2. Relevant equations



    3. The attempt at a solution

    I expanded it to 45 + 6√15 + 6√21 + 6√35
    Should I collect like terms (the multiples of 6)? I don't know how to proceed from here. Thanks in advance for any help.
     
  2. jcsd
  3. Mar 27, 2012 #2
    I'm not sure, but I don't think this expression can be converted to the form A2+B2.
     
  4. Mar 27, 2012 #3
    Maybe it's because I forgot to mention that A & B may contain roots. I think it's possible because it is an assigned question. But I'm stuck...
     
  5. Mar 27, 2012 #4
    There are no real numbers that factor to the sum of two squares. Your answer will be imaginary.
     
  6. Mar 28, 2012 #5
    3[√3+√5+√7]^2

    3[√(1.5)+√(2.5)+√(3.5)]^2 + 3[√(1.5)+√(2.5)+√(3.5)]^2

    up in the middle of the night doing this.. so I may have broken a million rules getting to this point :blushing:
    You Might want to double check but they seem equivalent :devil:
     
  7. Mar 28, 2012 #6

    Mark44

    Staff: Mentor

    How about this?
    3[√3+√5+√7]2 = 2[√3+√5+√7]2 + [√3+√5+√7]2

    The original expression is now written as a sum of two terms. Can you finish the problem by showing that each of these terms is the square of something? I.e., can you identify A and B with the above being equal to A2 + B2?
     
  8. Mar 28, 2012 #7
    It only works with odd numbers

    (√1.5 + √3.5)2 + (√1.5 + √3.5)2 = (√3 + √7)2

    The left side is 2 * 9.58 = 19.16. The right side is 19.16


    (√44.5 + √6.5)2 + (√44.5 + √6.5)2 = (√89 + √13)2

    The left side is 2 * 85.014 = 170.029. The right side is 170.029

    yesh?
     
    Last edited by a moderator: Mar 28, 2012
  9. Mar 28, 2012 #8

    Mark44

    Staff: Mentor

    Yes, this works. My example (now deleted) was flawed in that I forgot to square the value on the right side. Apologies for the misdirection...

    Here's what's going on.
    (√1.5 + √3.5)2 + (√1.5 + √3.5)2 = 2(√1.5 + √3.5)2
    = (√2 *√1.5 + √2 *√3.5)2
    = (√3 + √7)2
     
  10. Mar 29, 2012 #9
    Hey no worries, Mark44, beside I found my version of the solution completely out of luck just bored and messing around with my calculator :P
    You're version of the sum of two terms is just as valid isn't it?
     
  11. Apr 4, 2012 #10
    How did I not notice that?! :rofl: That works perfectly Mark. Thanks to everyone for their help.
     
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