Question

Is the golden ratio a rational or an irrational number? (Hint: A rational number can be expressed as the quotient a/b of two integers, with the denominator b not equal to zero.)

Answer 1

Do you need a proof?

Answer 2

No, I jus need to know if its rational or not. Ive never been good with figuring that out.

Answer 3

\[\Large \varphi=\frac{1+\sqrt{5}}{2} \]
So, can you tell wether it's rational or irrational by this expression?

Answer 4

I would say irrational, but I could be wrong

Answer 5

you're right about that, it's not a clean proof or anything, but intuition wise it helps in my opinion (-:

Answer 6

Thanks! :)