Hi,

Prove or disprove that

a. sum of two distinct irrational numbers is irrational.

b. Product of two distinct irrational numbers is irrational

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- Aug 27th 2011, 07:26 PMMathsNewbie0811Proofs about irrational numbers.
Hi,

Prove or disprove that

a. sum of two distinct irrational numbers is irrational.

b. Product of two distinct irrational numbers is irrational - Aug 27th 2011, 07:30 PMProve ItRe: I need help for these questions
- Aug 28th 2011, 04:44 AMmr fantasticRe: I need help for these questions
- Aug 29th 2011, 03:08 AMHallsofIvyRe: I need help for these questions
Or simply $\displaystyle \sqrt{2}*\frac{1}{\sqrt{2}}= \sqrt{2}\frac{\sqrt{2}}{2}$ which was probably what Prove It intended.

- Sep 3rd 2011, 12:18 PMTinybossRe: I need help for these questions
I've always liked this proof that an irrational to an irrational power need not be irrational: consider $\displaystyle \sqrt2^{\sqrt2}$. If that's rational, then we have our counterexample; otherwise, a counterexample is $\displaystyle \left(\sqrt2^{\sqrt2}\right)^{\sqrt2}={\sqrt{}2}^{ \sqrt{2}\sqrt{2}}=\sqrt2^2=2$.