• Support PF! Buy your school textbooks, materials and every day products Here!

Number Theory. Argue Is not the square of an integer.

  • Thread starter celtics777
  • Start date
  • #1
22
0

Homework Statement


Argue that (17^4)*(5^10)*(3^5) is not the square of an integer.



Homework Equations


N/A?


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?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
955
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].)
 

Related Threads on Number Theory. Argue Is not the square of an integer.

Replies
2
Views
1K
Replies
5
Views
2K
Replies
5
Views
992
Replies
3
Views
1K
Replies
3
Views
15K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
1
Views
1K
Replies
8
Views
1K
Top