- #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

but how about the condition which X is odd number?

I have no idea of this

- Thread starter SOHAWONG
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- #1

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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

but how about the condition which X is odd number?

I have no idea of this

- #2

Hurkyl

Staff Emeritus

Science Advisor

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[itex]\sqrt{4}[/itex] is irrational?

- #3

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no,i may add despite 1,4,9,16,25...etc[itex]\sqrt{4}[/itex] is irrational?

- #4

Char. Limit

Gold Member

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[tex]\sqrt{x}[/tex] is irrational iff x=/=n^2 for n belonging to the integer set.

- #5

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yes, but how to prove?

[tex]\sqrt{x}[/tex] is irrational iff x=/=n^2 for n belonging to the integer set.

- #6

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- #7

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what does gcd mean?

- #8

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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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http://en.wikipedia.org/wiki/Square_root

http://en.wikipedia.org/wiki/Square_root_of_2

And for an interesting history of the discovery of irrational numbers look at

http://en.wikipedia.org/wiki/Irrational_number

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