How to prove √X is irrational number

  • Thread starter SOHAWONG
  • Start date
  • #1
16
0
when X is even number,it's easy to prove
but how about the condition which X is odd number?
I have no idea of this
 

Answers and Replies

  • #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
14,950
19
[itex]\sqrt{4}[/itex] is irrational?
 
  • #3
16
0
[itex]\sqrt{4}[/itex] is irrational?
no,i may add despite 1,4,9,16,25...etc
 
  • #4
Char. Limit
Gold Member
1,208
14
So in other words...

[tex]\sqrt{x}[/tex] is irrational iff x=/=n^2 for n belonging to the integer set.
 
  • #5
16
0
So in other words...

[tex]\sqrt{x}[/tex] is irrational iff x=/=n^2 for n belonging to the integer set.
yes, but how to prove?:confused:
 
  • #6
237
0
Fundamental theorem of arithmetic. Assume p^2/q^2=x with gcd(p,q)=1, and see what has to divide what.
 
  • #7
16
0
Fundamental theorem of arithmetic. Assume p^2/q^2=x with gcd(p,q)=1, and see what has to divide what.

what does gcd mean?
 
  • #8
237
0
Greatest common divisor. If gcd(p,q)=1, it means the fraction p/q is in lowest terms.

Look at the proof for sqrt(2), and adapt it. Remember that "even" just means "is divisible by 2", so that if you're checking a number other than 2, you won't be thinking about "even" anymore.
 

Related Threads on How to prove √X is irrational number

  • Last Post
Replies
10
Views
2K
Replies
9
Views
3K
Replies
22
Views
21K
  • Last Post
Replies
12
Views
15K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
6
Views
908
Replies
6
Views
3K
Replies
11
Views
25K
Top