# Thread: Even Func and Irrationality

1. ## Even Func and Irrationality

Hello, I have questions regarding:

a) Let k be any integer. Prove that if k^3 is even, then k is even.

b) Prove that 3√2 is irrational. Hint: Mimic the proof that √2 is irrational and apply the result from part (a).

c) Suppose two numbers a and b are irrational. Must the sum a + b be irrational? Justify your answer with an appropriate proof or counterexample

Thanks for helping

2. Originally Posted by mms6
Hello, I have questions regarding:

a) Let k be any integer. Prove that if k^3 is even, then k is even.

b) Prove that 3√2 is irrational. Hint: Mimic the proof that √2 is irrational and apply the result from part (a).

c) Suppose two numbers a and b are irrational. Must the sum a + b be irrational? Justify your answer with an appropriate proof or counterexample

Thanks for helping
a) Prove the contrapositive. Assuming k is odd, prove that k^3 is also odd.

c) $\displaystyle a = 1 - \sqrt{2}$ and $\displaystyle b = 1 + \sqrt{2}$