Thread: Proofs 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

Originally Posted by MathsNewbie0811

Hi,

Prove or disprove that

a. sum of two distinct irrational numbers is irrational.
b. Product of two distinct irrational numbers is irrational

a) Use a simple counterexample, like

b) Use a simple counterexample, like ...

Originally Posted by Prove It

a) Use a simple counterexample, like

b) Use a simple counterexample, like ...

I suspect the OP's use of the word 'distinct' implies 'different'.

@OP: and provide the necessary counter example for disproving the statements in both (a) and (b).

Or simply which was probably what Prove It intended.

I've always liked this proof that an irrational to an irrational power need not be irrational: consider . If that's rational, then we have our counterexample; otherwise, a counterexample is .