How to prove √X is irrational number

  • Thread starter SOHAWONG
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  • #1
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Main Question or Discussion Point

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
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[itex]\sqrt{4}[/itex] is irrational?
 
  • #3
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[itex]\sqrt{4}[/itex] is irrational?
no,i may add despite 1,4,9,16,25...etc
 
  • #4
Char. Limit
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So in other words...

[tex]\sqrt{x}[/tex] is irrational iff x=/=n^2 for n belonging to the integer set.
 
  • #5
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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
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Fundamental theorem of arithmetic. Assume p^2/q^2=x with gcd(p,q)=1, and see what has to divide what.
 
  • #7
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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
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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.
 
  • #9
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