1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Number Theory. Argue Is not the square of an integer.

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Argue that (17^4)*(5^10)*(3^5) is not the square of an integer.

    2. Relevant equations

    3. The attempt at a solution
    Do I break these up, and show that each is not a square? I'm not sure if that would be correct, but sqrt(17^4)=289 * sqrt(5^10)=3125 * sqrt(243)=15.5884 =...

    Since sqrt(243)=15.5884 and is not an integer then the above is not the square of an integer. Is this an efficient explanation?
  2. jcsd
  3. Sep 5, 2012 #2


    User Avatar
    Science Advisor

    Well, it certainly doesn't show any understanding of the problem! Look at the exponents: [itex]\sqrt{17^4}= (17^4)^{1/2}= 17^2[/itex]. [itex]\sqrt{5^{10}}= (5^{10})^{1/2}= 5^5[/itex]. What about [itex]\sqrt{3^5}[/itex]?

    Do you see why the fact that 3, 5, and 17 are prime numbers is important?
    (Consider the same question about [itex]\sqrt{(8)(18)}[/itex].)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook