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# Square roots watch

1. How to prove that the square root of a non perfect square is irrational.
So I guess it's showing that if .
2. (Original post by Ano9901whichone)
How to prove that the square root of a non perfect square is irrational.
So I guess it's showing that if .
Meh, you can do better than that, you can prove that if then is either an integer or irrational. I'll go ahead and prove that instead.

Proof 1: Let with and hence then is a contradiction.

Proof 2: Rational root theorem gives us that the rational roots of must be of the form with and . So the root must be either an integer or irrational.

Proof 3: I'll let you consider other methods.
3. (Original post by Zacken)
Meh, you can do better than that, you can prove that if then is either an integer or irrational. I'll go ahead and prove that instead.

Proof 1: Let with and hence then is a contradiction.

Proof 2: Rational root theorem gives us that the rational roots of must be of the form with and . So the root must be either an integer or irrational.

Proof 3: I'll let you consider other methods.
How does your proof explain why cube root of 8 is rational? So when a=8 and b =3 ?
4. (Original post by Ano9901whichone)
How does your proof explain why cube root of 8 is rational? So when a=8 and b =3 ?
The proof merely says that is either an integer or irrational, obviously, since 2 is an integer, we are done.

For some clarification, my proof(s) show that is rational if and only if for some .

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